The 27-year-old scored the Gunners second goal to secure all three points.
“We concentrated from the first minute until the last minute. We believed in ourselves and we knew that we had made massive mistakes in the first two games,” Özil told Arsenal player.
“Today was our last chance – we had to win. We did that and now we’re back in the game. We’re all the happier for that. We showed heart and the fans supported us superbly. The most important thing is the three points.”
The Gunners went into the game having lost their first two games of the group stages against Dynamo Zagreb and Olympiakos which left them bottom of the group.
Had the north London based club lost against Bayern Munich it would more than likely have meant an early exit from the competition but the Gunners have now managed to give themselves a glimmer of hope at progressing to the Last 16.
The 27-year-old also scored and provided an assist against the Red Devils before the international break in the Premier League.