The Gunners were reduced to ten men when Laurent Koscielny was sent off for wrestling Edin Dzeko to the ground in the 10th minute before James Milner and Dzeko had City ahead inside 35 minutes. Vincent Kompany was also sent off for a late challenge on Jack Wilshere
Wenger believes that his players did not fire from the beginning and admitted he was frustrated with their stuttering performance.
"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," he said.
"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."