The Gunners' Champions League hopes are dangling after the German giants convincingly conquered them in the Round of 16 first leg at the Emirates Stadium but Wilshere refuses to concede defeat even though he admits the North Londoners were punished.
"We didn't start great and against good teams you get punished," the England midfielder told ITV1.
"In the second half we stepped it up and showed we could play but it's unfortunate we didn't do that in the first half. We could have got one with Giroud but it was a good save and they nicked another one.
"It'll be tough away but we're not out of it yet."
Toni Kroos and Thomas Muller gave Bayern a two-goal lead early in the first half before Lukas Podolski got one back for the Gunners in the 55th minute but Mario Mandzukic killed off the game with just under 15 minutes remaining. The return tie takes place at Munich's Allianz Arena on March 13.