After Manchester United's 2-1 win over Liverpool earlier in the day, the pressure was on Roberto Mancini's men to deliver or end the weekend 10 points down in the Barclays Premier League title race.
The visitors were handed an advantage when referee Mike Dean sent off Arsenal defender Laurent Koscielny for wrestling Edin Dzeko to the floor after just 10 minutes.
Although the Bosnian saw his penalty saved, via the post, City - who had last won in the league at Arsenal in 1975 - took command with first-half goals from James Milner and Dzeko.
Arsenal, whose defeat saw them lose more ground on the top four, regrouped after the break, but were not able to find a way back into the game - even when City captain Vincent Kompany was sent off with 15 minutes left for a two-footed tackle on Jack Wilshere.
Wenger felt Arsenal, who will be without midfielder Mikel Arteta for around three weeks with a calf injury, paid for a meek approach.
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 on Sunday afternoon, 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.