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."
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 added: "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."
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%."