Arsenal manager Arsene Wenger branded his players "timid'' after they slumped to a 2-0 defeat against Manchester City at the Emirates Stadium.
He said: "Overall we started too timid, with not enough authority in a game like that, and allowed them to dictate. We paid very early for that.
"We didn't start with enough confidence or authority. You have to dictate your personality, especially defensively.
"It is frustrating because the team showed great heart and desire after that, but we were a bit too nervous to play in a serene way at home and that is costing us.''
Wenger added: "The players want to do well, it is just the fact that we need to be a bit more confident in this kind of game.
"We want to do so well, that we are a bit uptight.
"It is not anger, it is frustration that we do not see from the start what this team is capable of.''
Wenger had not yet reviewed Koscielny's red card when he spoke on Sunday night, insisting that would not change the outcome.
"What do I make of the decision? That is not really important. You have to live with the decision,'' the Arsenal boss said.
"I was surprised, but honestly. I refuse to watch it again because what does it help now?
"I will watch it again. I have heard it was a penalty. Was it a red card? I don't know.''
Abou Diaby came into midfield, in his first appearance since September because of a thigh injury.
Wenger revealed Spaniard Arteta could be set for a length spell on the sidelines.
"He has a scan on Monday, [he will be out for] approximately three weeks. It is a strain on his calf,'' the Arsenal boss said.
"Of course [it is a blow]. In midfield he gives us stability, experience and tactical knowledge. We will miss that.''
Wenger maintains Arsenal are "in the market'' for January signings, but will only move for quality targets.
"We try very hard, believe me. We have a team around me who analyse everything. We select targets, I watch them, but it is difficult to speak about any names,'' he said.
City, meanwhile, are to appeal Kompany's red card, shown after the defender clattered into Wilshere with feet raised, although the sliding challenge did win the ball.
"We will appeal, because it is impossible that we can lose one player for three games for nothing. It is not red card, it is nothing,'' said City boss Mancini.
"He went into the tackle, anticipating the opponent and took the ball before.
"I don't know how it is possible to get a red card like this. It was no foul, no red card.
"He went in with one foot, that is a tackle. If you want to be right and just, we can say what has happened - if it was a red card, I would say, but it was not a red card, because he anticipated Wilshere. Totally, 100%.''
Kompany took to Twitter to give his side of the story, accompanied by a photo which appeared to show one of his feet being on the floor as he made the tackle.
"No grudges against the referee, I understand the difficulty of the job,'' he said.
City remain seven points behind United, and Mancini insists all is not yet lost.
"At this moment, United play very well, but the season is long. It is important for us to be there, close with them, and we will arrive the moment they lose points,'' he said.
"We have the derby on April 6 and we need to arrive there with five or four points behind, it is okay.''