Germany forward Podolski opened his account in Sunday's 2-0 Barclays Premier League victory at Liverpool and immediately set his sights on more goals and points for his new club.
The Gunners lost star striker and captain Robin van Persie this summer but Podolski told their official website, www.arsenal.com: "When I'm on the pitch, I can win matches."
He added: "I'm very happy to score my first goal at Liverpool with their amazing fans and stadium. I'm also very happy that we won and got the three points.
"You must always work hard in matches. You must fight, you must run and you must score goals."
Podolski's goal was also Arsenal's first of the season following scoreless draws against Sunderland and Stoke.
He said: "We played very well in the first two matches. But when you don't have the three points, the press write that you play no good. But I think we played very well - we just didn't score a goal.
"This is the Premier League and you must fight and run. This is my style of football - I like the style of Arsenal."
Meanwhile, former Arsenal defender Mikael Silvestre has been training with his old club to keep up his fitness following his release by Werder Bremen.
There have also been reports the Gunners are preparing to offer a new contract to England winger Alex Oxlade-Chamberlain.
Source: PA
Source: PA