Arsenal are competing on three fronts to end their long wait for silverware, with Arsene Wenger's side top of the Premier League, into the last 16 of the Champions League, and through to round five of the FA Cup.
Friday's 4-0 home win against Coventry, in which Podolski scored twice, was Arsenal's seventh victory in a row in all competitions.
And Germany striker Podolski is enjoying the quest for trophies.
"It was an important match for us, the FA Cup is important trophy for the club and in England," he told BT Sport.
"I think the first half was very good, the second half the last 10 minutes was good.
"The second half we did not play so well and we needed to keep going and create chances for 90 minutes.
"We were a bit slow, Coventry had a few chances. If they had scored at 2-0 we would have been in trouble. But we are in round five and top of the league, it is a long season but we want to stay there and fight for trophies.
"We have an important match against Bayern in the Champions League, we're top of the league, we want to stay there and keep fighting."