The 29-year-old completed his £24 million move to Old Trafford after refusing to sign a new deal with the Gunners earlier this summer.
Wenger admits he doesn't like how the situation has unfolded but the Frenchman did praise Van Persie's professionalism and his commitment to the club during his time at the Emirates Stadium.
“I am not a specialist on time healing but there will be a frustration [among some fans] of course,” Wenger told the club's official website.
|NOT GUNNER DO IT
|7/5||Arsenal are 7/5 to finish outside the top four with Paddy Power|
“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 per cent 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.”
It's not the first time a key member of the Arsenal team has moved on for a bigger salary and promises of silverware but the 62-year-old is confident the Financial Fair Play regulations will even out the playing field.
“It is a concern,” he admitted. “But you say we live outside of reality? No, we live in the economic reality that other clubs do not. There are some things we cannot afford to do, it is as simple as that.
“Honestly, I think it is a short-term problem - the world cannot go on like this. You cannot imagine that the world will go on just splashing money out without any return because people will get tired of that as you’ll only have a few clubs competing with each other.
“[Financial Fair Play] will make a big difference, how quickly I cannot answer because I am not responsible for putting it in place.”