The London club were dealt an early blow when Lauren Koscielny was dismissed after 10 minutes for tugging Edin Dzeko down in the box.
While the Bosnian striker saw his penalty saved via the post, City, who had last won in the league at Arsenal in 1975, soon took command with first-half goals from James Milner and Dzeko.
The result saw Arsenal fall six points from fourth place, and while City's Vincent Kompany saw red for a poor tackle on Jack Wilshere after the break, the home side couldn't find away back into the tie.
Ultimately, Wenger felt Arsenal paid a costly price for their meek approach in the match.
He said: "Overall we started too timid, with not enough authority, 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 confident in this kind of game.
"We want to do so well, that we are a bit uptight.
There was more woe for Wenger too, as he revealed Mikel Arteta could be sidelined with a calf injury for up to three weeks.
He said: "Of course it is a blow.
"In midfield he gives us experience, stability and tactical knowledge. We will miss that."