The Gunners fell behind after just five minutes against Liverpool and were 2-0 down, before roaring back to draw 2-2 at the Emirates on Wednesday.
It was the fifth time in a row they had gone behind in Premier League games this month and leaves them short of a top-four spot.
But Podolski said: "We must fight for a Champions League place. It felt like we won three points against Liverpool, to be 2-0 down and come back like that.
"We are in the FA Cup and the Champions League but the focus must be on the Premier League. We want third place."