Erik ten Hag warned Manchester United "are still far away" from challenging the Premier League elite, despite beating Arsenal on Sunday to make it four wins in a row.
Two second-half goals from Marcus Rashford, after Bukayo Saka cancelled out debutant Antony's opener, gave United a 3-1 victory over their old foes at Old Trafford.
The Red Devils have collected a maximum 12 points from their past four matches in their best run of form in the league since April 2021 under Ole Gunnar Solskjaer.
United have defeated Arsenal and Liverpool during a streak that has taken them from bottom of the division into fifth, but Ten Hag does not believe his side are title contenders.
"We have to get better if you want to win trophies in the end," Ten Hag said.
"I understand fans that they dream and, of course, the standards of Man United has to be high, but we are all in the start of a process. We are still far away.
"We have to get doing things much better than we do now. And that is an investment. We have to go that way together every day, bringing that high standard to [the training ground at] Carrington.
"The players know we have to get better if you want to win trophies in the end. What we have to do is win every game."
Ten Hag made a change to his starting line-up for the first time in four matches by bringing in new signing Antony in place of Anthony Elanga.
United had less possession (39.5 per cent) than Arsenal and a smaller expected goals (xG) return of 1.35 compared to 1.45 for their opponents.
The hosts managed to pick up another victory, however, and Ten Hag feels his side will only get stronger after spending more time together on the training ground.
"We have to invest in training and in meetings in order to get that in games," the Dutchman said. "We are just at the start of a process.
"Casemiro has only just arrived; Antony has just got here; Cristiano Ronaldo missed pre-season, so we have to get that practice in.
"Once we do that we'll be able to control games better. In the process we will dictate games. There's a long way to go but we are going in the right direction."
United's improved form comes on the back of losing their opening two matches against Brighton and Hove Albion and Brentford, conceding six times and scoring just once.
They are only the third side in Premier League history to win four in a row after losing their opening two, after Tottenham in the 2011-12 season and Arsenal in 2018-19.
"From day one we have set high standards and values," Ten Hag added of his side's recent performances. "We work hard to create a winning culture.
"I'm not now thinking we are at that point, but we are on our way, heading in a good direction and have to keep this going.
"We'll continue pushing the attitude and mentality by setting high standards every day. Good is not good enough – we have to do better and I think there's room for improvement."
Fonseca: Milan have 'respect' but 'are not afraid' of Juventus
Paulo Fonseca said Milan have plenty of "respect" for Juventus, but his side "are not afraid" of their rivals ahead of their Serie A clash on Saturday.
After a slow start to the season, Milan are six points adrift of Juventus in the table, but only a place behind them, as they aim to make up the ground on the top six.
The Rossoneri have played a game less than Thiago Motta's side, and could catapult themselves back into the Scudetto picture with a win this weekend.
Milan return to the San Siro for the first time since a 2-0 defeat to Napoli at the end of October, and could register two consecutive home defeats in Serie A for the first time since between October and November in 2023.
"It is not decisive, but it is important, like all of them," Fonseca told reporters ahead of Saturday's game.
"I can't say that the game against Juve is more important than the next one against Empoli because we need consecutive victories.
"It's a different game, but I always think positively. We are Milan, we have a lot of respect for the 'Bianconeri', but we are not afraid. We are here ready to win."
A boost for Milan is that Juventus will be without top scorer Dusan Vlahovic for Saturday's clash after returning from international duty with a muscle problem.
Despite the Serbian's absence, Fonseca was aware of the danger his probable replacement, Timothy Weah, would pose, having managed him during his time at Lille.
"Juve knows how to adapt very well. I don't know if Weah will play," Fonseca said.
"Weah is very fast and attacks deep, not like Vlahovic. It will not be the same thing of course.
"We will have to pay attention to movements in depth and less to support work, because he is a player who does less of this job."
While Fonseca has endured a stuttering start to his tenure at the San Siro, Milan have shown they have the ability to match the very best.
They beat rivals Inter in October before stunning Real Madrid at the Bernabeu in their last Champions League encounter, keeping their play-off hopes alive.
"I believe it's a matter of motivation and not pressure," Fonseca said.
"Against Inter, Juve and Real it is easy to be motivated, it's more difficult to go to Cagliari and have the same motivation.
"Pressure is always with us, every day. If we don't want to have pressure, then we shouldn't be here."
'Right guy at the right time' - Amorim confident of changing Man Utd's fortunes
Ruben Amorim believes he is the "right guy at the right time" to turn Manchester United's fortunes around.
The 39-year-old signed a two-and-a-half-year deal earlier this month to keep him at Old Trafford until June 2027, replacing Erik ten Hag after he was sacked in October.
Amorim is the sixth permanent United manager since Alex Ferguson retired in 2013, having left Sporting CP to take charge during the international break.
He won two Primeira Liga titles as Sporting head coach as well as two Taca da Liga trophies, while he led the club to a perfect start in the league this season, winning all 11 of their games.
United sit 13th in the Premier League table ahead of their trip to Ipswich Town on 15 points, though they are just four points behind Chelsea in third.
Amorim recognised the size of the task ahead of him in Manchester but is confident he can make a change.
"I'm a little bit of a dreamer and I believe in myself, and I believe in the club," he said during his first press conference.
"I think we have the same idea, the same mindset and that can help.
"I truly believe in the players; I know you don't believe a lot, but I do. I want to try new things. You guys don't think it's possible, I do.
"Call me naive, but I believe I am the right guy at the right time. I truly believe I am the right guy."
Aged 39 years and 302 days, Amorim will be the youngest to take charge of his first match for the Red Devils since Wilf McGuinness in August 1969 (31y 288d).
United have won just four of their 11 league games so far this season, and have struggled in front of goal, netting just 12 times so far.
Expected to implement his favoured 3-4-3 formation, Amorim admitted it would take time for the club to adapt and has asked for patience as the players get used to his tactics.
"I know at Manchester United we have to win games. We need a lot of time because it's a tough league, we have to improve a lot to try to win the title," he added.
"We have to change the physical aspect of the team. I don't know how long it will take."
Vlahovic out of Juventus clash with Milan
Dusan Vlahovic will miss Juventus' trip to Milan in Serie A this weekend and is also a doubt for the Champions League game at Aston Villa, head coach Thiago Motta has confirmed.
Vlahovic returned from the international break with a muscle problem in his left thigh, and the manager, after he confirmed the Serbian's absence for Saturday's game at San Siro, was asked about his chances of playing on Wednesday at Villa Park.
"I don't know. He definitely won't be there tomorrow. We hope to have him back as soon as possible," Motta told a press conference on Friday.
"Injuries are part of football. Now it's Vlahovic's turn, but we'll keep playing with the same principles, attacking and defending together."
Vlahovic is the latest of Motta's injury problems at Juventus. Argentine winger Nicolas Gonzalez missed the last six league games and is still unavailable, while Poland striker Arkadiusz Milik is a long-term absentee.
Brazilian midfielder Douglas Luiz will also miss the game with Milan and defender Juan Cabal recently suffered an Anterior Cruciate Ligament (ACL) injury, the same issue which will keep fellow defender Gleison Bremer out for the rest of the season.
"I'm really disappointed for Cabal because, like Bremer, he'll be out for a long time," Motta said.
"This is another reason to push ourselves, to commit that bit more so that these absences don't weigh too heavily."
Juventus go into the game as the only unbeaten side in Serie A but find themselves sixth in the standings in what is so far a very tight title race, with just two points separating Motta's side from leaders Napoli.
"It's very balanced and this is good for both us and the public," Motta said.
"We must all try to continue like this. We have to try to get as many positive results as possible."
Milan are one place behind Juve but six points off Motta's side.
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