The Germany international scored a brace in the Gunners' 3-1 victory over West Ham on Tuesday night, a win that sees them leapfrog Everton into fourth place in the Premier League.
Arsene Wenger's side booked their place in this season's FA Cup final with Saturday's win over Wigan, but Podolski says they should forget about their Wembley showpiece and focus on qualification for Europe's elite competition.
"The FA Cup is after the season. We'll leave that for the moment and focus on the Premier League," he told Sky Sports.
"Everyone wants to play in the Champions League because of the atmosphere, the matches are amazing and they are important for the club as well.
"Every player wants to play in the Champions League, but we must understand that we have hard matches to come - we play away at Hull City and Norwich. It's not easy but if we win all of our matches we'll qualify."
The German's first goal of the game came from a superb Santi Cazorla assist in the 44th minute - with Podolski reserving special praise for his Spanish team-mate.
"Everyone knows he is an amazing player. He can play the final ball and see a pass between three or four players," he said.
"Not a lot can pass like that, it was a great pass and it was important before half time. The three points stay at the Emirates and now we focus on the next game."
Cazorla, who received the man-of-the-match award, believes it's pivotal that Arsenal fully recover for their trip to Hull City - their third game in eight days.
"The most important thing tonight was to win. We need to win all of our games but we must recover for Sunday - it's difficult to play every three days," he said.
"The most important thing was to win and to get ready for Sunday."