The 27-year-old signing from Koln and fellow newcomer Santi Cazorla both got on the scoresheet and helped the Gunners overcome a lacklustre Reds side.
However the Polish-born attacker has warned his side they must build on this impressive display if they are to compete with the Manchester giants vying for the title.
|14/1||Arsenal are 14/1 with Bet365 to beat Southampton next Saturday
Podolski said: “The Premier League is very hard to win. It is not like Spain, where only Real Madrid and Barcelona fight for La Liga.
“In the Premier League, you have five or six teams who want the title. We are one of those and must fight for it. We have 35 matches more and must play in all of them like we did at Liverpool.
“I’ve had a lot of managers, I think 10 of them. But Arsene Wenger is a great coach, one of the best in the world.
“Before I came, I spoke to him about the style of the club, the football he wants us to play. Our first goal showed what I mean – good passing, running, keeping the ball and then scoring the goal.
“This style of Arsenal is my style. I like this. We are a team that likes to pass the ball, playing one or two touches. But to win in the Premier League you must also be prepared to fight and to run. We did this well.
"I have been asked to play on the left, but you can see that I am free to leave that position and play inside. I don’t just have to play wide, I can go in the middle to link up with Abou or Santi. With Santi, in training, I’ve loved the way it has gone. All the time we work on this, one and two touches.
“You could see that for our goals at Liverpool. He passed to me for the first one, and then I gave the assist to him for the second.
“But we have only played three matches and must keep on improving.”
The Germany international believes the team must reproduce the performance at Anfield against less glamorous opponents if they are to have any chance of fighting for silverware.
Podolski continued: “When you have played teams like Sunderland and Stoke and not picked up three points in either game, you have to expect headlines saying you’re no good.
“It is what I have been used to, no matter whether I’m playing for Koln, Munich or Arsenal. If you don’t win the matches you have to expect there will be a negative atmosphere. We are a big club and we want to win every game.
“From the first two matches we only picked up one point each game, which was not good enough. But if we play like we did at Liverpool, then we will fight for the title.”