The Netherlands international has joined left-back Mikael Silvestre as the only other footballer to have been managed by both coaches and has acknowledged the rarity of the experience.
Van Persie also recognised the other high-profile managers who have guided him during his 11-year professional playing career.
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"I have had special coaches all in their own way," Van Persie told OnsOranje.
"[Bert] van Marwijk, Wenger, [Marco] van Basten, Ferguson. Piece by piece they are special.
"I think I have been [one of] the only players ever who has worked under Wenger and Ferguson. That's special."
Van Persie was signed by Sir Alex last month, after notching 37 goals for Arsenal last season, and has already scored four goals in three games for his new side – including a hat-trick in the 3-2 win over Southampton last Saturday.
However, the striker also missed a penalty during that game at St. Mary’s, a moment which still frustrates him despite going on to win the game in injury time.
“A career won't be always a bed of roses. You have disappointments," he continued.
"Look at my missed penalty kick against Southampton last Sunday. That is what you call a disappointment.
"Taking a penalty kick in that way when you are 2-1 behind. That's just bad.
"I couldn't explain it, not even to myself. And what you do next? Do you stay disappointed? Or are you going to hunt, and get over it?
"In the game I put it behind me, thankfully. Many people can get swept up after something like that. It's happened to me [before] and it's all over then.
"Someone who is 18 years old wouldn't score two times after it. I wouldn't have done a couple of years ago.
"You have to be lucky, but you also have to force it."