Trailing 5-1 from the first leg, Arsenal pulled a goal back through Theo Walcott in the first half before Koscielny was sent off in the 54th minute for a challenge on Robert Lewandowski.
Lewandowski scored the subsequent penalty and Bayern ran riot against Arsenal's 10 men as Wenger's side limped out of the competition in the last 16 for the seventh season running.
"We produced the game we wanted and we were really unlucky," Arsenal manager Wenger told BT Sport at the Emirates Stadium. Some of the decisions of the referee were very difficult to understand. Lewandowski's offside, there's no penalty.
"On top of that, you get the red card. Of course, that killed us. After that, it was very difficult for us to finish the game.
"It's difficult to understand what happened. My team has produced a huge effort and played very well." Greek referee Tasos Sidiropoulos initially chose to book Koscielny, before showing the French centre-back a red card after consulting with the official behind the goal.
"It's just not serious," Wenger said. "When you see the importance of the game and you see an attitude like that. I'm absolutely revolted and sorry for the people who paid a lot of money to watch this game."
A group of around 200 Arsenal fans marched in protest against Wenger prior to the game and some supporters held up "WENGER OUT" banners at the final whistle.
Asked if the protesting fans reflected the mood at the club, Wenger replied: "No, not at all. I have nothing to add."