The last-16 first-leg loss exposed the lack of strength in depth which has contributed to the Londoners going out of both domestic cup competitions, lying fifth in the Premier League and looking poised to bow out of Europe.
Bundesliga leaders Bayern had the luxury of bringing on Dutch World Cup runner-up Arjen Robben and prolific Germany striker Mario Gomez in the second half but a glance at Arsenal's bench showed no such riches and Wenger's hands are largely tied.
The Frenchman, at Arsenal since 1996, failed to bring in attacking quality in the January transfer window and the club look doomed to an eighth season without a trophy, leading fans to question whether they still have the right man in charge.
The indefatigable Jack Wilshere is carrying the team almost alone but the midfielder jumped to the defence of Wenger, who won three Premier League titles in 1998, 2002 and 2004.
"It's nothing to do with the manager - he puts us on the pitch, it's down to us to perform," he told reporters.
"The players have to take responsibility, we're man enough to take it. The manager has been here 16 years and he's done a great job so you can't question him."
However, celebrity fans such as British U.S. talk show host Piers Morgan and golfer Ian Poulter are among those to have called for Wenger's departure and it is difficult to see what the manager can do to ease the pressure.
First-half strikes from Toni Kroos and Thomas Mueller already had Arsenal against the wall but Mario Mandzukic's bizarre third goal after Lukas Podolski had pulled one back against his old club means last-16 progression looks impossible.
Not even a 2-0 win in Munich in three weeks' time will be enough, though that looks highly unlikely given Arsenal's current naivety in defence and fickleness in attack.
Thomas Vermaelen, still easily Arsenal's best centre half despite some lapses this term, had to switch to left back following Wenger's bungled attempts to fill the role and that left Per Mertesacker coming back into the heart of the backline.
The tall German lumbered about like a zombie butler in a horror movie, a pale imitation of the man Bayern would have remembered from his Bundesliga days.
Midfielder Aaron Ramsey again looked out of his depth and main striker Theo Walcott proved for the umpteenth time that despite a lucrative new contract he is not the finished article.
Arsenal's best hope came from substitute Olivier Giroud, who had one decent chance to cut the deficit.
However, the striker is hardly in the class of Robben and Gomez despite a great season with French champions Montpellier.
Wenger has had money to spend yet decided not to and has watched his nervous side lose in the League Cup quarter-finals to fourth-tier Bradford City and go out of the FA Cup last weekend after a woeful 1-0 home loss to second-division Blackburn Rovers.
They are four points off the fourth and final Champions League spot in the Premier League and if Wenger cannot reach that goal with his limited means for manoeuvre, the calls for change will reverberate around the Emirates.
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