Wenger was under pressure heading into the game following the FA Cup loss to Blackburn Rovers, and the Gunners are now on the brink of a European exit after conceding three away goals at the Emirates Stadium.
However, Wilshere believes that it is time for the Arsenal squad to take responsibility for their recent disappointments.
The England midfielder told ITV: "It's nothing to do with the manager, he puts us on the pitch, it's down to us to perform.
"The players have to take responsibility, the manager has been here for 16 years and he's done a great job. There's always a chance [in the second leg], we take it to their place, and we need a few goals. We have the players to do it, we just have to start better."
The second leg will take place on March 13 in Munich.