The Gunners were 2-0 down inside the opening eight minutes at Wembley Stadium before Cazorla's spectacular goal on 17 minutes reduced the deficit.
"[Cazorla's goal] was very important because we came straight back," Podolski told the club's official website. "It was a nice goal, a free kick and it was very important for us to come back, and we had the quality. The FA Cup is special and you must fight until the end.
"It means a lot when you play for a club like Arsenal and you win nothing for nine years, so it is something special for us players, the manager, the club and for the fans. Let's celebrate the FA Cup!"
Saturday's triumph saw Arsenal lift the FA Cup for a record-equalling 11th time.