The Germany international has scored three times in five games for the Gunners as they look to plug the gap left by the Dutchman's departure to Manchester United.
Podolski scored in Arsenal’s 6-1 demolition of Southampton last weekend and, despite Van Persie's exit, the 27-year-old is already feeling at home in north London.
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"For me it was better if he had stayed," Podolski told The Daily Mirror. "He is a world-class player and I hoped that he stayed and we played together but he made a decision and it is the team of Arsenal that is important.
"When I came on the first day to the club everyone made it easy for me.
"Not only the team but those around the team: the coaches, the physios, the president and all the staff make it easy for me. I feel happy at Arsenal. It is good for me.
"The team and Arsene Wenger make it easy on the pitch. Last week we played very well. This is the style of football that I like - we play with one or two touches."
Podolski is happy with the way he has started his Arsenal career, but refuses to get carried away with ideas of scoring a hatful of goals and winning trophies in his first season.
"When you are playing up front you want to score goals and like to score goals," he added. "When you score goals you are very happy for yourself and for the team.
"I don't know about targets - we will see. We have only played four or five matches and I have three goals and I am very happy about the good start for me and for the team.
"We must keep fit and well - it is a long, long season and we don't have a break in the winter like in Germany.
"We must carry on playing like the last few matches and we must keep on fighting."