The Premier League side dominated the opening stages of the last 16 tie in front of a fervent Emirates Stadium crowd, but Mesut Ozil missed tamely from the penalty spot in the ninth minute following a foul by Jerome Boateng.
Bayern defender David Alaba then missed a penalty of his own in the 40th minute, but Arsenal were still punished as the incident resulting in that spot-kick saw goalkeeper Wojciech Szczesny sent off for a foul on Arjen Robben.
Toni Kroos, the outstanding player of the match, opened the scoring with a superb curling strike nine minutes into the second period and substitute Thomas Muller headed a late second to reward wave after wave of pressure from the reigning European champions.
"Tonight everything went against us because I think we should have been three up before they got a sniff in the game," Wenger told Sky Sports.
"The spirit was absolutely fantastic. The penalty we missed killed the crowd and the positive vibes a little bit.
"After we were down to 10 men and had one player (Kieran Gibbs) injured you cannot change anymore and you know that you will suffer physically.
"Overall it's a very difficult night but, as well, a night when the team has shown some quality and some class.
"But at the end of the day we lost the game."
Defender Per Mertesacker believes Arsenal's improved team spirit means that they should not be written off in Munich.
Last season, Arsenal conceded a 3-1 first-leg advantage to Bayern at the same stage of the competition. Although the scoreline is broadly the same, Mertesacker was still buoyed by the way the European champions were pinned back in the early exchanges - in stark contrast to when they ran riot on their last trip to the Emirates.
The Germany centre-back also takes encouragement from the subsequent 2-0 triumph in last term's away leg.
"When you look back at last year, we lost here 3-1," he said. "It was a bit worse than now so we are looking forward to Munich, and why can we not repeat that from last year?
"Munich, they are a fantastic team, they play possession very well. We tried everything today, especially in the first 10 minutes.
"We deserved that first goal but overall we have to take that defeat and reverse it in Munich. There are regrets to the second goal but we are stronger than last year."
