With the Gunners needing to overturn a 5-1 deficit from the first leg, they lost by the same result to crash out of the Champions League by a 10-2 aggregate scoreline.
Theo Walcott put Arsenal into the lead early on and was denied a penalty when clashing with Javi Martinez soon after, while Laurent Koscielny was dismissed before the hour mark for a foul on Robert Lewandowski in the penalty area.
"We produced the game we wanted and we were really unlucky with some decisions by the referee which are very difficult to understand," he told BT Sport.
"When we were 1-0 up, it was 100 per cent a penalty on Walcott. The red card, of course, killed us and the game. After that it was very difficult for us to end the game.
"My team has produced a huge effort tonight and played very well."
Koscielny was initially shown a yellow card for his push on Bayern striker only for the referee to give the defender his marching orders following discussions with the official behind the goal.
Wenger bemoaned the decision, insisting Lewandowski was offside in the build-up, as Arsenal suffered their worst ever loss at the Emirates Stadium to exit the Champions League at the last-16 for the seventh year on the trot.
He continued: "Lewandowski was offside [when he was fouled], then there is no penalty, then he gives a yellow card, then a red card! It's just not serious!
"When you see the importance of the game and then an attitude like that I'm absolutely revolted.
"I'm sorry for people who come and pay a lot of money to watch these games.
"I felt we were in it and you never know how Bayern would have reacted if we scored the second goal. [The scoreline] looks very bad and does not reflect the quality of our performance.
"Once it was 2-1 down it was very difficult and we had no chance to qualify any more. That's not the part of the game I would like to keep in my mind as the second part of the game has been spoilt by the referee."