Zlatan Ibrahimovic apologised for the red card that cost Milan dearly in their Coppa Italia exit to rivals Inter, coach Stefano Pioli has revealed.

Ibrahimovic, who had scored his 499th club career goal to give Milan the lead, was sent off for a second bookable offence as he felled Aleksandar Kolarov just before the hour-mark.

Romelu Lukaku equalised from the penalty spot soon after and Christian Eriksen's stoppage-time free-kick settled a controversial Derby della Madonnina encounter.

Ibrahimovic had earned his first yellow card in a confrontation with former Manchester United team-mate Lukaku.

The two forwards went head-to-head in a heated exchange that saw Ibrahimovic aim offensive language in the direction of his opponent.

It was a major misstep and Milan paid the price for Ibrahimovic's ill-discipline, but the 39-year-old was apologetic, according to his coach.

"Ibrahimovic apologised. He knows he created a problem for the team," Pioli said. "He apologised because he is a great man and champion.

"It's clear that the game was more difficult one man down in a game so balanced. It has been crucial. It wasn't supposed to happen but it happened unfortunately.

"We felt the fatigue in the last 30 minutes and we didn't achieve a positive result.

"We wanted it and we prepared for it. Now we go back to the league and to Bologna."

Milan remain top of Serie A, two points ahead of second-placed Inter, as they aim to end a 10-year wait for the Scudetto.

Stefano Pioli wants to see a reaction from his players in the Coppa Italia showdown with Inter following Milan's humbling home loss to Atalanta last time out.

The Serie A leaders went down 3-0 at home to Gian Piero Gasperini's side on Saturday, though they still have a two-point cushion over their next opponents at the halfway stage of the 2020-21 season. 

Next up is the small matter of a derby against Inter on Tuesday, an opportunity for Milan to quickly move on from such a disappointing result and reach the semi-finals of the Coppa Italia. 

The Rossoneri came out on top when the teams met earlier in the season, Zlatan Ibrahimovic's early double proving enough in a 2-1 triumph. 

"It's a different competition, but one we care about. The league is a different story," Pioli told the club's official website ahead of the game.  

"The next derby will be in a month, with other important games beforehand, so this is just a Coppa Italia match. However, it is an important quarter-final we need to face in the best way. 

"As always, there are opponents to face, dangerous opponents, but we are determined to bounce back with a good performance.  

"The Coppa is a competition we care about and aim to win, because in the end all the big teams in the league find themselves in this position, facing off in the quarter and semi-finals.   

"We weren't particularly lucky in the draw. We are in the toughest section, but if you want to win the Coppa, you have to face everyone.  

"It's important to us and we'll do our best to win."

Pioli confirmed Ismael Bennacer is not quite ready to return - the midfielder is on course to be available for Saturday's trip to Bologna, though - while Hakan Calhanoglu is also still out.

New recruit Mario Mandzukic suffered an issue at the weekend after making his debut as a second-half substitute, albeit the striker has not yet been ruled out entirely.

Milan have not lifted the Coppa Italia since 2003, while their last Scudetto arrived a decade ago. Pioli appreciates there is pressure to succeed, particularly after a strong first half to the campaign, but insists that is all part of the job when in charge of such a big club.

"Last Saturday reminded us that if we can't maintain our level, we run the risk of losing against these opponents," he added.

"So, our objective is to make an even greater effort, a more determined one to try to maintain our standing through until the end of the season. 

"We want to be ambitious and win all our games. When we don't, we work even harder to make sure the situation doesn't happen again.  

"That's why pressure is a privilege we must live with, or rather we must want this pressure because we're at a great club - pressure and expectations are a part of that."

Inter beat Juventus. Juventus beat Milan. Milan beat Inter. For once it has been tough to predict the title race in Serie A.

Winning the Scudetto was not enough for Maurizio Sarri to keep his job at Juve last season, meaning Andrea Pirlo is under significant pressure as the Bianconeri chase a 10th straight league crown.

However, they have struggled to convince under the former midfield metronome and sit seven points adrift of leaders Milan in fourth, although they hold a game in hand.

There has seemingly never been a better chance for Inter, who are two points off top in second, and Milan to end Scudetto droughts that date back to 2009-10 and 2010-11 respectively.

Fans and pundits will continue to have their say on who will sit top come the end of the season, and the Stats Perform AI team have also crunched the numbers to predict the champions for the 2020-21 campaign.

With the majority of the 20 teams having reached the halfway stage of the league campaign, they have simulated how the rest of the season may play out.

The data model estimates the probability of each match outcome – either a win, draw or loss – based on each team's attacking and defensive quality.

Those ratings are allocated based on four years' worth of comprehensive historic data points and results, with more weighting given to recent matches to account for improvements or declines in form and performance trends.

The AI simulation takes into account the quality of the opposition that a team scores or concedes goals against and rewards them accordingly.

All that data is used to simulate upcoming matches using goal predictions from the Poisson distribution – a detailed mathematical model – with the two teams' attacking and defending ratings used as inputs.

The outcome of the season is then simulated on 10,000 different occasions in order to generate the most accurate possible percentage chance of each team finishing in their ultimate league position.

Without further ado, let's have a good look at the results of the simulation with the predicted final league table.

INTER END JUVE'S REIGN

Although they sit second at the halfway stage, our model predicts Inter will end Juve's dominance of Serie A.

Inter have a 35.7 per cent chance of topping the table for the first time since their treble-winning campaign of 2009-10 and it is projected they will do so by a two-point advantage.

Not only do Milan surrender top spot to the Nerazzurri, they slip behind Juve into third with the top three separated by just three points. It would still represent their best finish since 2012-13.

Juve's chance of retaining the title is deemed to be 23.1 per cent, marginally better than Milan's 21.6 per cent.

ATALANTA RETURN TO CHAMPIONS LEAGUE

Gian Piero Gasperini steered Atalanta to Champions League qualification for the first time in their history in 2018-19 and made it back-to-back top-three finishes last season.

They are predicted to return to Europe's premier club competition by finishing fourth, edging out Napoli – they even have a 6.8 per cent chance of pulling off an unlikely title win.

Gennaro Gattuso's side have a 17 per cent probability of snatching the final Champions League qualification berth, with Atalanta's prospects narrowly superior at 17.4 per cent.

Roma are predicted to fall from their current position of third down to sixth but that is still good enough for them to deny arch-rivals Lazio qualification to the inaugural Europa Conference League.

The top six may need to beware of Sassuolo, Hellas Verona and Sampdoria, however. Sassuolo have a 0.3 per cent likelihood of finishing inside the top four, while Verona (0.6 per cent) and Sampdoria (0.3 per cent) also have an outside chance of stealing European qualification, though our predictor suggests Lazio will finish 12 points clear of Sassuolo in seventh.

GENOA AND TORINO ESCAPE DROP

At the turn of the year Torino were rock bottom with one win from their opening 14 games and Genoa were in the relegation zone with them.

However, Torino and Genoa have both moved out of the bottom three by claiming six points and eight points respectively over their past five games.

The two sides are predicted to maintain strong enough form to stay out of the drop zone, with Crotone (20th), Parma (19th) and Cagliari (18th) projected to suffer relegation to Serie B.

It is by no means a guarantee, though. Genoa are only 0.2 per cent more likely to come 17th than they are to suffer relegation by finishing 18th, while Torino's differential between 15th – where they are predicted to place – and third-bottom is 2.7 per cent.

Stefano Pioli insisted Milan had "nothing to be ashamed of" after an imperious Atalanta side condemned them to a second Serie A defeat of the season.

Having seen their unbeaten start to the campaign ended by Juventus on January 6, the Rossoneri suffered a second loss in four league games as they fell 3-0 to Atalanta at San Siro on Saturday.

Cristian Romero, Josip Ilicic and Duvan Zapata scored in a one-sided victory that stretched Milan's winless run against Gian Piero Gasperini's side to seven in the top flight.

However, Milan were confirmed as winter champions as Inter's 0-0 draw at Udinese means they will be top of the table even after each side in the league has played 19 games.

Pioli watched his team muster just two shots on target as a club-record run of scoring in 38 consecutive league games came to an end.

But the coach sees little reason to be overly concerned about losing to the reigning champions and an Atalanta side who have recorded 36 points from their first 19 matchdays, their best return in a 20-team division.

"We started well, with a lot of players in attack," he told Sky Sport Italia.

"They played very well. I'm disappointed with how we conceded the first goal from a dead ball, and the second one killed the game.

"It wasn't supposed to be like that, we could have done more, but we didn't manage it. Atalanta's strong points were evident, but we had to play better from a technical point of view.

"They were stronger than us tonight, but we're strong regardless. A game like this can happen. We know the league is competitive and difficult.

"I think defeats to Juventus and Atalanta are nothing to be ashamed of. Atalanta were physically superior, more intense, winning all the duels and the second balls as well.

"It's tight when you reach this level. We'll analyse the defeat, try to see where we can improve and focus on the next match."

Milan face Inter in the Coppa Italia quarter-finals on Tuesday before heading to Bologna next Saturday in Serie A.

Stefano Pioli said Zlatan Ibrahimovic exceeded expectations with his brace in Milan's 2-0 win over Cagliari on Monday.

Ibrahimovic scored a brace as Milan moved three points clear of rivals Inter atop Serie A.

The 39-year-old has found the net in nine successive starts for the first time in his career in Europe's top five leagues as he moved onto 12 Serie A goals in eight games this season.

Milan coach Pioli said Ibrahimovic performed above expectations, with his side closing out a win despite Alexis Saelemaekers' 74th-minute red card.

"Ibrahimovic is a champion in everything he does. Of course, now that he is back, we have more options and qualities," he told a news conference.

"The more choices and strong players we have, the more likely we are to win games.

"He still surprises me, but now I know him so well. We always expect him to give the maximum, and today he exceeded our expectations."

Ibrahimovic had the most shots (five) and shots on target (three) against Cagliari, while no player was involved in more duels (17).

Milan extended their unbeaten run away from home in Serie A to 16 matches, which equals their most in the three-points-per-win era (since 1994-95).

"We are happy with today's performance. It wasn't easy to play on such a difficult pitch like this one, facing an opponent with great qualities," Pioli said.

"We deserved the victory and now we will start focusing on the next important game on Saturday against Atalanta."

Stefano Pioli confirmed Milan will consider adding further to their squad in January amid speculation Mario Mandzukic is set to join the club.

Mandzukic – who previously played in Serie A with Juventus – is a free agent after terminating his contract with Al-Duhail by mutual consent in July.

The Rossoneri are reportedly going to sign the Croatian striker on an 18-month deal, boosting their forward options as they look to maintain their push to win the league for the first time in a decade.

Pioli was not willing to discuss individual names at his pre-match news conference ahead of Monday's trip to Cagliari but did admit the club are ready to act if the right player becomes available.

"I don't want to and cannot comment on players that I don't have," he told the media. "I have a lot of confidence in the club and the management team. I leave that task to them.

"We know that if there is the possibility of strengthening the team, we will do it. We will be ready in January if there is the possibility of improving this group." 

Milan have already made one signing in the mid-season transfer window, midfielder Soualiho Meite arriving on loan from Torino.

"Meite makes a department that already had good solidity even more competitive," Pioli said of the new recruit.

"I really liked the move. We have combined quality and quantity. I also liked how he spoke, saying he was ambitious. To join our group, you have to be like that."

The Serie A leaders head to Cagliari without Hakan Calhanoglu and Theo Hernandez, both players currently isolating after testing positive for coronavirus.

Pioli admits it is a blow to be without the influential duo – they are also set to miss next Saturday's home fixture with Atalanta – but is confident he has the quality within his squad to cope with such situations during the course of the season.

"They are important absences, but this season is like that," the Milan boss said. "There are critical issues that can come at any moment, so we must always be prepared and attentive.

"The quality of the players that I will have available tomorrow will certainly make us have a good match.

"We are prepared, that's why I expect the players to always be ready. We can all be decisive and help the team."

Stefano Pioli was glad to see Zlatan Ibrahimovic get another 45 minutes under his belt in Milan's penalty shoot-out win over Torino.

Ibrahimovic, 39, made his return from injury off the bench against the same opponent in Serie A on Saturday, but started and played 45 minutes three days later as Milan reached the Coppa Italia quarter-finals with a 5-4 penalty shoot-out victory.

Milan head coach Pioli was happy to see the forward, who has scored 10 goals in seven Serie A matches this season, get more game time after being out for seven weeks.

"We wanted to give him a longer time compared to the previous championship game. We preferred to let him play from the beginning due to his characteristics," he said, via Sky Sport.

"This time will be used to improve his condition in view of the next championship match."

The clash at San Siro finished 0-0 before Hakan Calhanoglu scored the decisive penalty in the shoot-out after Ciprian Tatarusanu had denied Tomas Rincon.

It meant Milan reached the Coppa Italia quarter-finals for the 12th consecutive season.

"I am lucky to have a team that knows how to fight, knows how to play, knows how to grit its teeth in a difficult match even for the qualities of our opponents," Pioli said.

"For the many occasions we had, we could have avoided even reaching penalties, but we went beyond physical and mental fatigue and this is a desired qualification."

Milan, who are three points clear atop the Serie A table, visit Cagliari on Monday.

Stefano Pioli had no doubt Milan would produce an instant response to their setback against Juventus, though he was again left counting the cost of injuries and suspension following the win over Torino. 

Serie A leaders Milan saw their unbeaten league start come to an end in a 3-1 reverse in midweek, a game that saw Davide Calabria have to deputise in midfield. 

However, the Rossoneri continued their title tilt with a 2-0 triumph over Torino thanks to first-half goals from Rafael Leao and Franck Kessie. 

"I must admit, I was not at all surprised by this performance," Pioli told DAZN. 

"I know these lads and expected them to give this kind of a response. The first half was excellent, particularly in terms of quality, and we inevitably came under pressure during the second half against a Torino side in good form."

However, Leao will miss Milan's next game through suspension due to an accumulation of yellow cards, while Sandro Tonali left the game on a stretcher and Brahim Diaz picked up a knock. 

"We don’t have any news yet, we'll have to see, they both got nasty knocks," Pioli added of the injured duo. 

"What does disappoint me is losing Leao for the next game, because I've never seen a player booked for simulation in midfield. I don't think that was in any way fair or a real understanding of the situation." 

There was some positive news as Zlatan Ibrahimovic made his comeback from a calf injury late off the bench having been expected to play no part. 

"We knew that if he passed the final test tomorrow in training, he'd be ready for a small portion of the game," Pioli said. 

"The muscular injury is behind him now, we will see what to do in the Coppa Italia. Zlatan is unique, we hope to have him in full shape as quickly as possible."

Milan head coach Stefano Pioli claimed the experience of losing 3-1 to Juventus at San Siro was "healthy" for his side, saying: "We had not felt that for a while."

A Federico Chiesa double and a third goal from Weston McKennie ended the leaders' unbeaten Serie A record this season, consigning them to a first in 28 matches in the Italian top flight.

Milan had 20 shots, but Davide Calabria's equaliser late in the first half was the only one to find the back of the net and Pioli admitted his side were second best on the night.

"We have to tip our hats and give credit to our opponents for managing to get back in front," Pioli told Sky Sports Italia.

"We did what we needed to, created chances and inevitably allowed some, but after going behind for the second time, it became more difficult to get back into it.

"It was a very even game up until the second Juventus goal and I feel that's the moment that changed it.

"We were penalised by their quality in situations where we could’ve been a little more concentrated."

The defeat came on a night when Milan's closest title challengers and city rivals Inter were beaten 2-1 at Sampdoria.

Despite seeing his players miss the chance to go four points clear at the top of the table, Pioli reflected on the positives.

He said: "The lads had their heads down in the dressing room and were disappointed, but in a way it was healthy for us to experience defeat, as we hadn't felt that for a while.

"I gave them a pat on the back, said they ought to be proud of what they achieved in the circumstances.

"We proved that we are a strong team tonight."

Zlatan Ibrahimovic has been ruled out of the Serie A clash between Milan and Juventus on Wednesday.

The 39-year-old striker has been sidelined since being substituted in the 3-1 win at Napoli on November 22.

The former Manchester United and Paris Saint-Germain star has missed seven league games for the Serie A leaders, although the Rossoneri have fared well in his absence, winning five and drawing two of those matches.

Stefano Pioli's side are alone in Europe's top five leagues in that they have not lost a top-flight match since the 2019-20 season was initially shut down from last March.

They head into the match with champions Juve at San Siro knowing a win would move them 13 points clear of the Bianconeri, who are fifth with a game in hand.

Ibrahimovic had offered hope he could be fit to face his former club after recent injury trouble, posting training footage to social media on Monday with the caption "Tick tock tick tock".

Head coach Pioli, though, says the player is not fully fit and admitted to scolding him for causing a stir two days before the game.

"I told him off because, after that footage, I was peppered with phone calls," Pioli told reporters.

"He is better and he's working well, but he won't be in the game tomorrow."

Rafael Leao has performed well in Ibrahimovic's absence, scoring in the 2-1 win at Sassuolo and the 2-0 victory at Benevento in the past two and a half weeks, becoming the second-youngest foreign player to reach 10 Serie A goals for the club, behind only Alexandre Pato.

Pioli believes the 21-year-old's development is a sign of the way Milan have improved in the past year. The Rossoneri have taken 37 points from their first 15 league matches this term, the first time they have done so in the history of the competition in the three-points-per-win era.

“He’s growing a lot, he has characteristics that we must try to enhance in the right way," said Pioli. "The important thing is to see the will to grow and improve on a daily basis.

"All matches are opportunities to prove our worth. We have to concentrate on the game and raise our level because they are strong opponents, with experience, and they have been winning for years.

"We're showing we can play for it and we'll therefore play to win. We have scored 17 points more than last year. This is the right path, but we can't speak of a decisive match after 15 rounds."

Stefano Pioli lauded Milan's "heart, intensity, passion and belief" after they beat Benevento 2-0 to return to the Serie A summit despite playing for nearly an hour with 10 men.

Franck Kessie's penalty gave the visitors a first-half lead at Stadio Ciro Vigorito but Sandro Tonali's dismissal before the break left the Rossoneri up against it.

An inventive finish from Rafael Leao gave Milan a much-needed two-goal cushion early in the second half, with Gianluca Caprari missing a spot-kick at the other end for the wasteful hosts.

The win marked a fine response to Inter's 6-2 thrashing of Crotone earlier on Sunday, which had temporarily dislodged Milan from top spot.

But with his side now leading the way by a point, Pioli was full of praise.

"We showed heart, intensity, passion and belief. It's another very big victory," he told Sky Sport Italia.

"We don't let the results of our opponents put pressure on us. We put pressure on ourselves by demanding the best.

"There were a few errors, but we showed such unity to bring the result home.

"Every result is important to boost the self-belief."

Tonali was shown a red card after a careless lunge on Artur Ionita, with referee Fabrizio Pasqua upgrading his punishment from a yellow after reviewing the incident on the pitch-side monitor.

"I hugged Sandro in the locker room, he was sad about leaving the team down to 10 men," said Pioli.

"The issue with VAR is that things look much worse when slowed down compared to the dynamics of the movement, but Sandro will learn from this."

Next up for Milan is the visit of champions Juventus, though Pioli insists the result will not be pivotal in the title race.

"I think it'll be a great game between two teams in excellent shape," he said.

"I continue to say Juventus, Inter and Napoli are the strongest sides in Serie A, we just have to keep going along our path.

"It's not decisive or the passing on of any baton. Juve won the last nine titles and aren't far behind us at the moment.

"I continue to maintain we can talk about other things when we look at the table in April and if we are still in this position. Our strength has been to take it one game at a time, so we don't want to change that attitude.

"We are missing some important players, Tonali will be suspended, so it's going to be tough against Juventus. Whatever happens, it won't be decisive."