Arsenal were reduced to 10 men after just 10 minutes when Laurent Koscielny was shown a straight red card for hauling down Edin Dzeko in the box.
The striker missed the resulting spot-kick but a dominant City took the lead through James Milner and Dzeko then made it 2-0 before the break.
The Gunners battled hard after the interval but failed to make the breakthrough, before Vincent Kompany’s late red card for a reckless challenge on Jack Wilshere.
Wenger, whose side are now sixth in the Premier League table and 21 points behind leaders Manchester United, conceded that the Gunners were made to pay for a sloppy start to the game.
“Overall we started too timidly, with not enough authority in a game like that, and we allowed them to dictate from the start,” he said. “We paid very early from it.
“We didn’t start with enough confidence or enough authority. When you play at home in a game like this you have to dictate your personality, which we did not do, especially defensively.
“After that, we played 80 minutes with 10 against 11 against a good team, and it’s difficult. But then again, on both of goals I think we could have done better.
“It’s frustrating because the team afterwards showed great heart, gave everything and showed great desire, but we’re a bit too nervous to play in a serene way at home and that shows in the way we start the games.”
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