The 35-year-old Dutch striker will retire from football at the end of the season after returning to boyhood club Feyenoord, where he made his debut aged 17.
Van Persie won the FA Cup with Arsenal and a Premier League title for Manchester United during his time in England, but courted controversy among Gunners supporters when he penned a public letter in 2012 stating that the club's ambition did not match his own – before joining United that summer for £20 million ($25m).
“It’s really hard for fans,” Wright told Goal.
“I do feel for Robin because he was so unfortunate with injuries at our club and he stayed as long as he could, he saw people leaving around him.
“Being an ex-player I can totally understand [his decision to leave] but coming from a fans' point of view you can see why they would be very, very disappointed with the fact that he left and he went to Manchester United and won the title with them.
“Let’s face it, he won the title literally single-handedly for them. They would have loved him to stay and be fit enough to try and do that for Arsenal but it’s very difficult to say you want the fans to forgive him when he left and did exactly what he left for.”
Wright compares the Van Persie situation to the abuse he received from fans when he made the switch from Crystal Palace to Arsenal in 1991, for what was a club record fee at the time.
“It’s like when I left Crystal Palace. I love Crystal Palace but the fans have a problem with me simply because I left and went to Arsenal and was a success. I said to them I’m leaving to win trophies," added the ex-England international.
“Robin van Persie left talking to us about the ‘little boy’ in him who said he had to take this chance. He was totally justified in doing that because he won a Premier League medal.
“For anybody to expect Arsenal fans to welcome him with open arms is something that I can’t answer. There’s a certain loyalty that fans will want and unfortunately for Robin he just got himself into the situation where the greatest club in this country came calling with one of the greatest managers in world football – and it’s very difficult to turn that down.”
Ian Wright was speaking in partnership with YouTube. To check out his brand new YouTube channel, please head to www.youtube.com/ianwright