José Mourinho questioned whether some of his players were able to cope with the pressures of the Manchester derby, accusing them of “really poor individual performances” after a 2-1 defeat that finished with him heavily criticising the referee, Mark Clattenburg, as well as his own team.

Mourinho was incensed that Clattenburg did not award his team a penalty and show a red card to Claudio Bravo after Manchester City’s new goalkeeper, at fault for Zlatan Ibrahimovic’s goal, dived into a challenge on Wayne Rooney 11 minutes into the second half.

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However, the Manchester United manager also turned on his own players for the first time since taking the job in the summer. Henrikh Mkhitaryan was substituted at half-time on his first start since signing from Borussia Dortmund. Jesse Lingard was also substituted during the interval but Mourinho said there were other players who had performed badly.

“I didn’t change after 20 minutes because I didn’t want to destroy the players,” Mourinho said. “I didn’t want to make three changes at half-time, but if it was a sport with a free number of changes I would have done it after 20 minutes. I made a couple of decisions [with the starting lineup] because I thought the individual qualities of certain players would give me what I wanted. But I didn’t get it.

“But it is not just about them. We lost the ball very easily. Even our central defenders [Eric Bailly and Daley Blind], who were top-class until today, lost easy balls. What I told them at half-time was: ‘For some of you, it looks like you are trying to do what I told you not to do.’ I had told the players 20 times never to play a first-station ball – ‘never, because they [City] want to press, so never do that’ – and they did it 20 times.

“I think some of the boys felt the dimension of the game. Everything around the game – the derby, the big game, Man United, Man City, the focus, the attention. Some of the guys, they felt it. But it had nothing to do with inexperience or age because we have the kid [Marcus Rashford] in the second half and the kid looked like he was playing in the under-18s against Salford City. It’s about the individual and how everyone reacts to the dimension of the occasion in different ways. It’s difficult to predict.”

Facebook Twitter Pinterest Claudio Bravo challenges Wayne Rooney. Photograph: Tom Jenkins for the Guardian

Kevin De Bruyne had opened the scoring for City and Kelechi Iheanacho doubled their lead in the 35th minute before Ibrahimovic capitalised on Bravo’s mistake to score the goal that set up a thrilling second half. Bravo, signed from Barcelona to replace Joe Hart, had a difficult debut but Pep Guardiola was supportive of his new signing.

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“Claudio Bravo’s personality showed me a lot today,” the City manager said. “Sometimes when that happens maybe the player can think: ‘It is my fault.’ Instead Claudio said: ‘OK, it’s football, we were unlucky, the situation is unlucky,’ and in the second half look what he did – he played again and again with the ball. He was amazing with his feet – saves, going to attack the ball. I am happy for him. It was not an easy first game, after two training sessions, coming here to Old Trafford, and to play with that personality means a lot.”

Mourinho was less impressed and thought the goalkeeper should have been sent off. “I know the rules of the game. It’s obvious it was a penalty and a red card for Bravo. If it was outside the box, a direct free-kick and a red card. Inside the box, it is more difficult [for a referee] because it’s a big decision and sometimes referees are like us, human, and think twice before big decisions.

“If he [Clattenburg] doesn’t think twice, it’s a penalty and a red card with a big possibility of 2-2 and a lot of time to go. We could have been talking about a completely different story. We were punished by our bad first half, my responsibility, and we were punished by Mark with his bad decisions in the second half.”