Van Persie was officially unveiled as a United player on Friday following the completion of his move to the Red Devils.
The Netherlands international striker's original contract with Arsenal was to run until the end of the 2012-13 season, but he made it clear over the summer that he was not keen to extend it.
Wenger acknowledges Van Persie's professionalism for Arsenal over the years and asks the club's supporters to remember their former captain fondly.
"I am not a specialist on time healing but there will be a frustration [among some fans] of course," said on the Frenchman on the club's official website. "He has played for us for eight years, you have to respect what he has done for our club, what he did last year.
"This is a situation that is a completely brutal reality of professional sport. Robin was captain of the team last year and I give him credit until the last minute of the whole season [because] he fought like mad.
"For me that is to be professional. He comes in afterwards and wants to go? I don't like it. But that is being professional again. But being professional until the last minute of his stay at the club.
"He gave 100% and last year he kept us [up] there - 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."
Arsenal will begin their Premier League campaign with a home game against Sunderland on Saturday.