The result means that the Gunners now face an uphill task to qualify for the quarter-finals of the competition.
Despite his admission that he is "very upset", the German international has told his teammates that they now need to turn their "focus" towards Saturday's Premier League clash against Aston Villa.
"Very upset about the result last night, we now must stay focus. Another important match on Saturday," he wrote on Twitter.
Podolski was Arsenal's goalscorer against the Bavarians.