The United manager hauled off Henrikh Mkhitaryan and Jesse Lingard at half-time and said it was only because he did not want to “destroy them” that he did not substitute them earlier.
But he saved his most trenchant remarks for centre-backs Daley Blind and, in particular, Eric Bailly, saying some players had shown signs they did not possess the requisite big-game temperament.
“We had problems with poor performances,” Mourinho told reporters at Old Trafford on Saturday.
“We lost the ball very, very easy. Even our central defenders, that were really top class until today, they lost easy balls.
“Back-passes, first-station passes, from Bailly to (Marouane) Fellaini, from Blind to (Paul) Pogba.
“We lost the ball in these kinds of positions. So it was not (just) Mickey (Mkhitaryan) and Jesse, it was much more than Mickey and Jesse.”
Pep Guardiola`s City took a deserved 15th-minute lead when Kevin De Bruyne beat Blind to Kelechi Iheanacho`s flick-on before steering a shot past David de Gea.
The same pair combined to double City`s lead, Iheanacho tapping in after De Bruyne`s low shot came back off the post.
An error from City`s debutant goalkeeper Claudio Bravo, who flapped at a deep free-kick from Wayne Rooney, allowed Zlatan Ibrahimovic to pull a goal back.
But although United improved following the half-time introductions of 18-year-old Marcus Rashford and Ander Herrera, they could not find an equaliser.”What I told them at half-time was that for some of you, it looks like you are trying to do what I told you not to do,” said Mourinho.
“I told Bailly 20 times, never play a first-station ball. Never. Because this is where they want to press. Never do that. He did it 20 times during the game.
“I think really some of the boys, they 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 felt it.