The duo were on target at Anfield in the Gunners' 2-0 victory in the Premier League, their first of the season.
"Of course it is good when new signings start well and score a goal," said Wenger. "Arsenal is a club that has had many great players, so the new signings have to convince people that they can follow and be the same.
"I'm sure that in time these new players we have brought in will prove to the fans that they have the ability to play for us.
"Everyone understood Cazorla would not need six months to settle in - I am pleased for him. For the first goal it was good to get Podolski in with a chance on his strong left foot."
Arsenal have now picked up five points from three matches in the league and have yet to concede a goal.