The Germany international netted the Gunners’ first with a spectacular long-range effort as they game from a goal down to secure an impressive win at Emirates Stadium.
But Podolski has told his team-mates that they can ill afford any more slip-ups if they are to secure Champions League football for next season.
“It was one game and we have three points which is important, but we have 15 games more to play,” said Podolski, who has 12 goals and nine assists to his name this season.
“It’s not about saying, ‘today Arsenal are back’, because we need more of these games and more of these points. Then I think we are back in the top four.
“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 to the next game in the FA Cup.”
Podolski, who joined Arsenal from Cologne in the summer, also believes that the Premier League is more gruelling than the Bundesliga.
“I think it is harder here,” he said. “You have tough games and then you see the league in Germany and there is only one team at the front – Bayern.
“I think the quality in the German league is very good now, not like five years ago. But I think the Premier League is a little bit better.
“When you look at the league now, we have 15 games to go and we must fight to get back into the top four.”