Podolski scored his first Arsenal goal in their 2-0 win away to Liverpool, and the German forward expects to go from strength to strength in the Premier League.
He said: "I'm very happy to score my first goal here at Liverpool with their amazing fans and stadium.
"I think we played well in the first two matches, but when you don't have the three points the press writes that you play no good.
"This is the Premier League and you must fight and run. We do this very well and we pass very well. This is my style of football, I like the style of Arsenal and we have the three points."
Arsenal will aim to secure their first home league victory of the season after the international break against Southampton on Saturday, September 15.