Carlo Ancelotti said Real Madrid were not dominant enough to deserve their 2-0 win at Real Sociedad on Saturday.
After a tight first half, which saw Los Blancos manage just two shots on target, they secured all three points thanks to second-half penalties from Vinicius Junior and Kylian Mbappe.
They were far from their best though, accumulating just 0.6 expected goals from 16 shots (six on target), while they just edged possession with 52%.
However, Ancelotti praised his players' resilience and was proud of how they were able to endure the home side's pressure.
"It was a complicated match. We didn't deserve to win, because Real Sociedad pushed us really hard," he told a press conference.
"We held on and suffered, showed character and a lot of commitment. I value that a lot because it's not easy to find commitment in a team with so much talent and quality, and today we did it.
"I leave very satisfied, and then we have to be self-critical in order to improve. It's a great opportunity for us to assess what we didn't do well but with three more points in the table."
Madrid are second on 11 points, one behind Barcelona who visit fifth-placed Girona on Sunday.
Ancelotti acknowledged his side were struggling with fatigue and poor form, but said it was to be expected due to a busy calendar, coming off the back of the international break.
The Italian said he saw improvement in Mbappe's performance as the France captain settles in at his new club, having scored his third goal for Madrid on Saturday.
"We can talk about all the problems in the world with this match, but the important thing was to get out with a win," added Ancelotti, who was without midfielders Jude Bellingham, Eduardo Camavinga, Dani Ceballos and Aurelien Tchouameni.
"We have to take into account that we are not at 100%. It's normal, we don't have four midfielders who are injured. I value a lot the work of those who have played.
"I see Mbappe fresher, more active. He's very dangerous and combines well with Vinicius and the other forwards. He is improving a lot. I liked his game a lot."
Madrid now turn their attention to their Champions League title defence which starts on Tuesday against Stuttgart.
Leipzig have 'everything you would want' – Celtic boss Rodgers
Celtic may be four points clear of RB Leipzig in the Champions League, but Brendan Rodgers is not underestimating the challenge that his side face on Tuesday.
The Hoops welcome Leipzig to Celtic Park on matchday four, for what will be the fifth meeting between the sides.
Leipzig have won three of the previous four encounters, with Celtic winning 2-1 in a Europa League match in November 2018.
While Leipzig, who are second in the Bundesliga, have lost all of their Champions League matches this term, Celtic bounced back from their heavy defeat to Borussia Dortmund by holding Atalanta to a 0-0 draw in their last European outing.
Rodgers' team come into Tuesday's clash on the back of a resounding 6-0 defeat of Aberdeen in the Scottish Premiership, but Rodgers knows his side are in for a stern test.
"Leipzig are no different to Borussia Dortmund and Atalanta," said Rodgers. "A top team. They have everything you would want - speed, power, technique.
"It's a brilliant challenge for us."
After conceding seven goals against Dortmund on MD2, Rodgers explained Celtic knew they had to step up.
"You always have to learn and be better and we were against Atalanta, a really outstanding team," said Rodgers, who were perhaps fortunate not to concede against the Serie A side, given they conceded 2.4 expected goals (xG).
"We'll look to bring our energy to the game but we also know we'll have to defend for good periods of the game, play with concentration and commitment like we did against Atalanta," he said.
"There will be moments when we press with aggression and moments where we have to be controlled. Top teams will push you back and you have to have resilience."
After a run of 12 home games without a win at Celtic Park in the Champions League between 2013 and 2023 (D3 L9), Celtic have won their last two home games. They last had three wins in a row back in November 2007 under manager Gordon Strachan.
"Home games are very important at this level and when you want the result the supporters can bring you closer to that," said Rodgers.
"What the noise generates here is absolutely incredible.
"We will also need that bit of patience as well because we have to be educated in our pressure.
"We've got ourselves into a really good position after three games and now we have another opportunity to show we can pick up a result against a top team."
Neymar does not believe latest injury is serious
Neymar does not feel his latest injury is anything to be overly worried about.
The Brazilian star had to be substituted off late on in Al-Hilal's 3-0 win over Esteghlal in the AFC Champions League Elite on Monday.
Aleksandar Mitrovic's hat-trick propelled Saudi Pro League giants Al-Hilal to a comfortable win, though it was soured when Neymar clutched his right thigh and left the field just 29 minutes after coming on as a second-half substitute.
It was only the 32-year-old's second appearance since he returned from a year-long lay-off due to a serious knee injury.
However, the former Paris Saint-Germain and Barcelona attacker allayed fears over a serious injury.
"It felt like a cramp, only very strong!" Neymar posted on Instagram. "I'm going to have some tests and I hope it's nothing too serious.
"It's normal for this to happen after a year, the doctors had already warned me, so I have to be careful and play more minutes."
Neymar has played only seven games for Saudi Arabia's Al-Hilal since joining from PSG in a blockbuster transfer last year.
Fonseca targets statement Milan win over Real Madrid
Milan have no need to fear Real Madrid and their coach Paulo Fonseca is targeting a statement win in the Champions League.
Despite having won more Champions League/European Cup titles (seven) than any other club apart from Madrid (15), it has been 17 years since Milan last lifted the trophy in 2007.
On the other hand, holders Madrid have won the Champions League six times since 2013-14.
But Fonseca sees no reason to fear Los Blancos at the Santiago Bernabeu, where Carlo Ancelotti's side were recently hammered 4-0 by Barcelona.
"We're playing against a team that aspires to win the Champions League every year and for us it's a great opportunity to grow," Fonseca said.
"We'll play without fear of anything, with courage, because we believe we can play a great game and do great things.
"I always transmit to my team the desire to win and tomorrow will be no different. Real Madrid are a great team, but we will go out there thinking about winning. After that, anything can happen, but that's the mentality.
"To win a match like this, we have to defend well, have possession of the ball and create dangerous situations. A match against Real Madrid is a chance to show the world our quality and the way we are growing."
Madrid are 12th in the 36-team Champions League table with six points, while Milan are languishing in 25th spot – just outside the play-off places – with three points after three games.
Fonseca explained Milan had carefully studied Barcelona's 4-0 win over Madrid in last month's Clasico.
"I saw the derby, it's impossible not to watch it. They are teams I like to watch and I paid close attention to the game," Fonseca said.
"We are different from Barcelona but it was important to see Real Madrid's intentions against them because Barca have a similar way of defending with us. We made the whole team watch the game.
"It is the match between the two clubs that have won the Champions League the most. There are many games in the continent that are big, but this one is obviously something special, a match between two clubs that are attractive.
"We hope to put on a good show for people who enjoy good football."
Milan are winless in their last three Champions League games against Madrid (D2 L1) since they won 3-2 in October 2009 with goals from Andrea Pirlo and Alexandre Pato.
Madrid have won five of their seven home matches against Milan in the competition (D1 L1), beating them 2-0 in the most recent such match in October 2010.
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