The Germany international inspired his side to all three points with one goal and three assists against the Hammers, to leave his side trailing north London rivals Tottenham by four points in the hunt for Champions League qualification.
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"There is enough time to get back in the top four, and a lot of points to play for," Podolski told reporters.
"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 has hit 11 goals in 28 appearances since his £11 million move in the summer, but has only completed the full 90 minutes on one occasion in the league.
However, the striker is refusing to kick up a fuss over his early withdrawals, and insists that the team is the most important thing.
"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 explained.
"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."