Wenger rejected suggestions Manchester United signing Van Persie would have won them on Saturday's game.
"You can never check that. We have played some draws at home with Van Persie, we have lost some games with Van Persie as well," Wenger said.
"However, it is true that last year in every game he found something special.
"I never denied that we lost a world-class player, that is very difficult to replace."