Wenger, who signed Van Persie from Feyenoord for £2.75m eight years ago, remained patient as the striker struggled with injuries and refused to criticise him for joining rivals United after an incredible 37-goal season.
"This is a situation that is a completely brutal reality of professional sport," Wenger said. "Robin was captain of the team last year and until the last minute of the season he fought like mad. That is professional.
"It is a miracle we finished third. A big part of the miracle is down to him and you have to give him credit for that. He prepared for every game the right way. When he played the game he was 100 per cent committed.
"At the end he chose to go somewhere else. OK, I don't like it, but that is being professional again. He is a boy, born in Holland. We have taken him from Holland and we have to accept that when a player is professional, he can move again."