The German forward scored and set up three as the Gunners thrashed their east London rivals 5-1 at the Emirates on Wednesday.
Arsene Wenger's side remain sixth in the Premier League but neighbours Tottenham are now just four points away in the crucial final Champions League position.
"There is enough time to get back in the top four, and a lot of points to play for," Podolski said.
"We must believe in our game and our players. After the two defeats against Manchester City and Chelsea, the atmosphere was not so good, but now we have won 5-1 and we look forward to the next game."
Podolski, an £11m summer signing from Cologne, has been deployed to great effect down the left, rather than in a preferred central attacking role, and has played a full 90 minutes in the league just once, but insists he is happy to answer any call from Wenger.
"When you are a footballer, you will not always play 90 minutes. Sometimes you are not happy, but this is not important for me," he added.
"I fight for Arsenal, for the club and team and this for me is important.
"We have a lot of great players. The coaches don't change the full-back or centre-back - you change always the positions in the front who create something.
"You have great players and it is not a problem when I am substituted."