Thomas Vermaelen reduced the deficit with a bullet header on 21 minutes, but the second-half onslaught from the shellshocked Gunners never came as the Latics moved five points clear of the relegation zone.
Wenger slammed his side's defending and also was left frustrated they could not replace Mikel Arteta quick enough when the midfielder hobbled off with an ankle injury which probably rules him out of next week's clash with Chelsea.
Wenger said: "We defended horrendously for the first and second goal. Everybody involved was included for the first and the second goal.
"On top of that we conceded a second goal with 10 men on the pitch. It took us too much time to change and it was absolutely unbelievable.
"After that we had a mountain to climb. I felt in the first half we had enough chances to come back to 2-2, but the second half we dropped our level, we lost our team play, our cohesion and tried too much individually. There was not enough petrol left in the tank anymore.
"We didn't see anyone who could make a difference."
Wenger added: "Chelsea is a massive and vital game for us. We need to recover from the massive disappointment of tonight first, then prepare mentally for the next one."