Wenger - who earlier this week hit out at a growing number of critics following a shock FA Cup exit at home to Blackburn - accepted the Gunners had been outclassed by the ruthlessly efficient Germans in the first leg of their last 16 European tie at the Emirates Stadium on Wednesday and regroup to mount a final push for Champions League qualification again next season.
An early strike from midfielder Toni Kroos handed the Bundesliga leaders a crucial away goal, which was doubled when Thomas Muller stabbed home from close range.
Arsenal, with England forward Theo Walcott initially deployed as central striker, rallied briefly in the second half after they reduced the arrears with a header from Lukas Podolski against his former club.
However, after substitute Olivier Giroud fired a great chance straight at Bayern keeper Manuel Neuer from point-blank range, the Germans cut through the home side again after 77 minutes as Mario Mandzukic scrambled in a third to effectively end the contest, and almost certainly Arsenal's last faint hope of ending an eight-season trophy drought.
Wenger must now lift his beleaguered players for the Barclays Premier League run-in, where they face crucial games against Tottenham and Everton in their bid to salvage something from the campaign - namely a top-four finish to again play among Europe's elite clubs next season.
"We will have two battles, but maybe the easier battle will be to be back in the Champions League," he said.
"However, we have to give everything to try and change things in the second leg.
"But let's not hide the truth: it will be extremely difficult against a team of that quality.
"We have to give our best and hope we have built our confidence up a bit more, because that belief will be needed."
Wenger added: "The quality of my players is there, but they are not getting reward for their efforts.
"I still have confidence in my players and in my team but on this evidence there is clearly work to be done.
"However, you have to give them (Bayern) credit for their class. In patches in the first half, it was a difference of quality in their display to ours."
Bayern manager Jupp Heynckes, meanwhile, hailed the "astonishing" form of his side following another imperious display.
He said: "Arsenal allowed us a few things in their defence, but we are in astonishing form and can punish even the smallest mistakes of the opponent.
"At times it was quite difficult for us, we had to work hard, but even when they were putting pressure on us, we coped well."
Heynckes' side were beaten in last season's Champions League final, held at their Allianz Arena home, by Chelsea.
However, despite looking well set for another shot at European glory at Wembley in May, the German remains pragmatic.
"You cannot afford to underestimate an opponent because in football, we have seen everything," he said.
"But in this season it is very difficult against us, you can see that with our position in the league, conceding just seven gaols, that is amazing.
"We are also in a position to score, so we have a good chance to progress.
"But if we were to progress Arsenal can still have options in the Premier League to make the Champions League, the team has potential and class."