The Gunners were on the back foot from the word go and were down to 10 men inside 10 minutes when Laurent Koscielny wrestled Edin Dzeko to the ground.
Wojciech Szczesny kept out the Bosnian's penalty but it was not long before the champions capitalised on their advantage - James Milner hammering home a fantastic angled drive and Dzeko doubling the lead on the half-hour.
Vincent Kompany was dismissed for a challenge on Jack Wilshere late in the day, but by that stage Wenger's men were well beaten.
The Frenchman told Sky Sports afterwards: "It was frustrating because we were down to 10 men with 80 minutes to play and you know it will be a difficult game.
"I felt we were a bit too timid at the start with not enough authority. We let them dictate the game to us in the first 10 minutes and we were punished. From then on, it became difficult but in the second half we had a good response and we had a chance to come back, but we didn't."
On the Koscielny incident, Wenger added: "I haven't seen it again. I was surprised by the decision but I've heard it was a penalty. We have to live with the decision and it doesn't mean that you have to lose the game.
"I felt we gave away two cheap goals away and when you are down to 10 men, if you keep it 0-0, you never know.
"The team gave a lot at the second half - you can't fault that, but I feel we are a bit nervous at home and lack that authority that makes you strong, especially at the start of the game.
"There are a lot of positives. I feel some players had outstanding games - Jack (Wilshere) is getting stronger and has found a little bit of acceleration again. (Abou) Diaby also became stronger and stronger."