Arsenal pulled off a remarkable 2-0 win but even becoming the first side to beat Bayern in four and a half months was not enough to progress because of a 3-1 first leg loss.
"To qualify is 180 minutes," said Wenger. "It's a bit similar to last year's situation against Milan, when we missed the first leg [and lost 4-0]. The regret we have is not this game against Bayern but the first game. You could see tonight the weight of that third goal that we gave away with four minutes to go. It's massive.
"We went close and I am very proud of the performance but as well I am very disappointed for everyone who follows Arsenal. When you look at our game tonight we have many regrets about the first game.
"I felt it was very feasible to knock Bayern out. We had a plan that we respected tonight. It went a bit for us on some occasions but overall we played well. The second goal came too late but we did have a few opportunities in the second half. Bayern defended very well.
"They were a very defensive team tonight and they stopped us from playing. We were under pressure because a bad performance would have been terrible for the morale and the pride of the team. The regret I have is that there is potential in the team and we are, of course, out of the competition."