In the build-up to the first game of his second stint as Manchester United head coach, Michael Carrick spoke about Old Trafford being "a magical place". Few imagined he would conjure up a performance against Manchester City so complete that Pep Guardiola admitted his team might have been beaten even if Diogo Dalot had been sent off in the opening minutes.

Carrick has now added Guardiola's name to a list of managers he has beaten as United head coach that also includes Unai Emery and Mikel Arteta. He has also drawn with a Chelsea side managed by Thomas Tuchel. As he left the pitch to the echoes of the song United fans created for him when he first arrived as a player in 2006, Carrick was able to reflect on a day that could hardly have gone any better. "It's a great start, there's no getting away from that," he said, smiling.

Carrick is not Ruben Amorim, clearly. It is just not his way to deliver soundbites that create headlines. He does not beam the same way as the Portuguese or pepper his media engagements with laughter. He has also been around long enough to not get too carried away by the outcome of one high-profile game. "Consistency is the key to any success," he said. "If you can find that you're on to a winner. We're not going to have games with the emotion and feeling that today brought. We all understand that. But there's definitely a standard and expectation we need to live up to. That's our challenge."

Carrick and his family remained season ticket holders at United even though it is over a decade since he played for the club. This season he has appeared as a pundit on TV and analysed his old side's games. He could not know Amorim would get sacked, nor that he would edge out his old boss Ole Gunnar Solskjaer and be given the chance of guiding United to the end of the season, but he had a view in the back of his mind about how to get the best out of United's players. It did not involve Amorim's three at the back. It did involve Kobbie Mainoo, the most obvious victim of Amorim's rigid approach, which even United's executives eventually felt was not helping the club achieve consistency.

"I've watched a lot," Carrick said. "We've got season tickets, so my family comes and I've come to a lot of games over recent times. You get to know the players and your own eye. Everyone has an opinion and there are your instincts. It's obviously something that clicks into gear when you think maybe it might be on my toes to do something about it."

The reward came through Mainoo's industry alongside veteran Brazilian Casemiro, in a midfield pair Amorim never really gave the impression he trusted. "Kobbie was great alongside Casa," said Carrick. "Between the two of them it gave us a foundation."

Then there was the performance of Harry Maguire, starting his first game since 8 November, helping central-defensive partner Lisandro Martinez dominate Erling Haaland to such an extent that Manchester City's xG of 0.45 was their second lowest in 364 Premier League games under Guardiola. "It was a big ask of H and credit to him," said Carrick. "We could take it for granted sometimes, what players do. He has literally trained for two or three days over the last eight or nine weeks, so it was a bit of a calculated gamble over how long he could play. But he has come through it and he was fantastic."

Carrick even gained plaudits from former skippers Gary Neville and Roy Keane, who have led the suspicion and criticism over his appointment in recent days. "Michael Carrick is in heaven," said Neville on Sky Sports. "Manchester City cannot believe it. Massive figures, [Gianluigi] Donnarumma, Rodri, Haaland shaking their head and the biggest of all, Pep Guardiola - stunned. They have been run ragged. "It has been a perfect afternoon for United," added Keane. "It is not as if they got lucky."

Former United striker Wayne Rooney told BBC Sport: "The fans have been starved of that over the last few years. I know it's only one performance but I think everyone could see how exciting that team can be. You hear everyone, especially us as ex-players, talk about the United DNA and that has just shown what it is. Work-rate off the ball, wingers getting back filling in and helping out the full-backs."

United hit the woodwork twice, had three goals disallowed for offside, and Donnarumma made four excellent saves. His reaction effort in the second half to deny Casemiro as he tried to turn home the rebound, after an initial stop from Amad Diallo, was so good that the Brazilian was left biting his shirt in frustration.

There has been a lot of talk this week about the managers United should be trying to get in the summer and that Carrick should be viewed purely as a stop-gap. Yet those opinions ignore the swell of emotion created by performances and results. For the first time in what feels like a very long time, Old Trafford reverberated to the noise of fans responding positively to a team giving their best and delivering on a gameplan that, in the context of this 40-game season, was enough to get a victory in a very important game.

"The players certainly fed off it," Carrick said. "They left the changing room unbelievably desperate to do well. I was almost thinking don't be too desperate because it can cloud your judgment and you make decisions because you're emotionally so invested in it. But they got the balance right and the supporters were incredible. "I said yesterday this can be a magical place. It does some funny things and to get that feeling was exactly what we want. It's something we need to build on. We're not getting carried away massively, but you've got to enjoy that feeling when you get it."

United impressed in all phases of play. Their 32% possession meant they spent large parts of the game defending but United still limited City to 0.45 xG. Out of possession, their 4-4-2 compact shape was executed with excellent coordination and intensity. The roles of wingers Amad and Patrick Dorgu stood out. Dorgu man-marked Rico Lewis, nullifying his influence as he moved into central attacking positions, while Amad often dropped into the defensive line to form a back five, marshalling Jeremy Doku well.

When City had the ball, United's 4-4-2 funneled them into wide areas, where they defended with four players. With the striker, central midfielder, winger and full-back all coming across, it was difficult for City to find the space to create anything of note. In attack, United played in a way that was true to their traditions, taking advantage of their speed and directness. The positioning of Bruno Fernandes and Bryan Mbeumo either side of Rodri posed difficult questions of City's defensive midfielder, while wide players in Dorgu on the left and Matheus Cunha on the right were able to combine for United's second.