Giggs takes charge of his final match at the helm on Sunday when United visit Southampton.
"I witnessed two team meetings as I came in a bit late," said Van Persie, who returned to the team after a seven-week injury lay-off.
"The one from the last game against Sunderland, and Tuesday's game, were incredible. They were Sir Alex-esque.
"He's been brilliant. And he put in some fantastic passes and almost scored after coming on. He's a legend and I think he shows that every day."