The Gunners drew 1-1 with the Bavarian giants in the second leg at the Allianz Arena on Tuesday night to go out of Europe's premier club competition 3-1 on aggregate.
Despite the loss, goalscorer Podolski felt it was a constructive performance from the north London side who now get to focus on the Premier League title pursuit and the FA Cup semi-finals.
"We take a little bit of confidence but in the end, we lost and we are out," Podolski told Sky Sports.
"We now look forward to our Premier League and FA Cup games.
"We fought to the end. We played a good second half but it's not enough to go to the next round.
"We are in the semis for the FA Cup and we are still fighting for the title.
"We have important weeks to go, so we play and we will see what happens."
Arsenal, who sit third on the league table, will now focus their attentions on this Sunday's north London derby with fifth-placed Tottenham at White Hart Lane.
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