Wenger and midfielder Samir Nasri were charged by UEFA after arguing with Swiss referee Massimo Busacca after the final whistle on Tuesday.
Wenger was angry that forward Robin van Persie was shown a second yellow card for shooting at goal immediately after being ruled offside. Arsenal lost 3-1 and was eliminated 4-3 on aggregate.
"We are out of the Champions League, we have lost one of our big ambitions, we have been punished with a lot of damages and on top of that, we have to say sorry to UEFA," Wenger said. "We have done nothing wrong. They organized the competition, they named the referees who come to the games.
When you have a football game of that stature, you cannot come out with decisions like that and show a lot of arrogance on top of that.
"We can all understand that we can make wrong decisions, but after that it becomes dictatorship. It's not any more common sense." On Wednesday, UEFA charged Wenger and Nasri with improper conduct. UEFA's disciplinary panel will hear the cases on March 17.
"A bit more humility would do UEFA some good," Wenger said. "To apologize for what happened would be much better than charge people who have done nothing wrong."