Louis van Gaal said Chris Smalling did not react "very smartly" as he was shown a second yellow card during Manchester United's derby defeat.
Smalling was booked for attempting to stop Manchester City goalkeeper Joe Hart kicking the ball clear after a half an hour, and in the 39th minute he was then sent off after an ill-judged tackle on James Milner.
Asked about the dismissal, Van Gaal said on the club's official website: "I didn't see the first yellow, but as a player if you know you have a yellow card you have to deal with that problem.
"I don't think he dealt with it very smartly because then we have 11 against 10 and that's the most difficult way you can play for 45 minutes."
The United manager, who had warned his players pre-match they must not get sent off, later told BBC Sport: "In a derby you have to be careful -- the second yellow card is a stupid yellow card. As a player you have to control your aggression.
"I didn't see the first yellow but with the second, you know you already have a yellow, so have to handle it differently. I said that to the players. You have to deal with that. You cannot do what he has done with the second yellow card. That is not very smart.''
When asked whether Smalling had apologised to his teammates, Van Gaal said: "He said it very humbly. You can only accept it. But nevertheless it was in my opinion not so smart.''
United also had to contend with injuries in defence, with Antonio Valencia filling in for Rafael at right-back and Marcos Rojo stretchered off with a dislocated shoulder. Van Gaal was also unable to call on Jonny Evans and Phil Jones due to injury, so midfielder Michael Carrick and youngster Paddy McNair filled in alongside Luke Shaw.
The makeshift back four was unable to prevent Sergio Aguero netting a winner on 63 minutes but, despite their problems, Van Gaal felt his players performed well at the Etihad Stadium.
"I said to the boys their willpower and labour were unbelievable and they can be very proud," he said. "The fans know the boys are willing to give everything for the shirt of the club -- but at the end of the game, we have zero points. In this sport, it is always the goals that count.
"We were so close in spite of playing with ten men. We had more chances [with 10 men] than in the first half. We are close but not close enough. We have 13 points out of 10 matches and Chelsea have a lot more, as do Manchester City so we have a problem.
"We need to improve and prove that we are not close but better. We will improve, that I promise."
United captain Wayne Rooney, who was making his return to action after a three-match suspension, agreed that progress is being made.
"The pace of us was causing them problems," he said. "You could see they started panicking at the end, kicking the ball long. We just couldn't get that moment in the final third to get the equaliser.
"You can see every week we are getting better and we're not far away from being back up there and being a very good team. It won't be long before we are."