The Germany international urged the club to look forward with their new stars such as himself, Santi Cazorla and Olivier Giroud.
While admitting he would have liked Van Persie and Song to stay at the Emirates, Podolski believes it's now time Arsene Wenger's side moved on.
"It would have been better [had Robin Van Persie and Alex Song stayed]," Podolski told the Daily Mail.
"But we have Cazorla and Giroud now. Great players have left but we have to look forward."
The 27-year-old has conjured up an instant connection with fellow summer signing Santi Cazorla and says he doesn't understand how the Spanish playmaker hasn't been playing at this level sooner.
"In the offence I like to play with Cazorla. You see this in the matches. I am looking for him and he is looking for me," he added.
"I like playing with him. I can't understand why he was playing for Villarreal and Malaga and not a bigger team earlier.
"I'm looking forward to playing the next four years with him."
The German has enjoyed a fine start to his Arsenal career with three goals already this season but has warned his fans it's still early to label him a hero.
"It is too early to say: 'Podolski is a hero'," he added.
"After only five or six games you cannot say: 'He's the best player and Arsenal are great.' I don't like this."After 20 matches and we have lost six matches everyone will be saying Arsenal is rubbish and Podolski is rubbish. We must wait. I signed for four years. Not for five or six matches."