Fan protests before the second leg of the last-16 tie called for an end to the Frenchman's 21-year reign in North London and the Bundesliga champions ruthlessly replicated the scoreline from last month's first leg at the Allianz Arena after Laurent Koscielny was sent off.
Theo Walcott gave the Gunners a deserved first-half lead but the wheels came off for Arsenal when Robert Lewandowski converted a 55th-minute penalty having been brought down by Koscielny when through on goal.
Goals from Arjen Robben, Douglas Costa and an Arturo Vidal brace followed as fans streamed out of Emirates Stadium in their thousands.
Asked what needed to change at Arsenal, having again neglected to answer questions about his future when his contract expires at the end of the season, Wenger said: "What needs to change at this club? What do you mean by that?
"I think this club is in great shape but is at the moment going through a very difficult situation. What needs to change is the result in the next game.
"You are always worried for headlines. I am here to speak about football, not about my future.
"Tonight I thought there was no uncertainty in our game, we played very well.
"It's difficult, when you are 5-1 down against Bayern and you have to score four goals.
"You are down to 10 men - if you go forward you know you will be caught on the counter-attack; if you don’t go forward people will say, 'why didn't you at least try to score goals?' It is an impossible situation."