Podolski, who scored twice tonight, told BBC Sport: "The Champions League is very important and we must focus on the next game to ensure that we can qualify. It was important to score before half time and for us to get a win in a local derby.
"The FA Cup is after the season, we leave it now and we focus on the Premier League because everyone wants to play in the Champions League. The atmosphere is amazing and it is important for the club."
Arsenal face fellow FA Cup finalists Hull City at the weekend.