The continental competition represents Arsenal's last realistic chance of winning a trophy this season after they were knocked out of the FA Cup and Capital One Cup by lower-league opposition.
Bayern scored three away goals to put themselves in the driver's seat ahead of the return fixture in Munich and add to the pressure on Wenger, but Wilshere insists that the Arsenal players must take responsibility.
"I don't think it's anything to do with the manager," Wilshere told ITV after the match at the Emirates Stadium. "He can put us on the pitch and motivate us, but we have to do it on the pitch, and at the moment we're starting badly and we're getting punished for it.
"I think the players will take responsibility. We're man enough to take it. He's been here for 16 years and he's done a great job, so for me you can't question him."
Wilshere refused to give up on Arsenal's chances of progressing to the quarterfinals despite the significant deficit the Gunners will need to overturn at the Allianz Arena.
"The players are man enough to take [responsibility] and we'll take it on the chin and move on to the weekend and the away leg," Wilshere said. "We have to get a few goals there, we know we need at least three goals, and we've got the players to do it. We just have to start better."