The Rossoneri were trailing 1-0 when the match official pointed to the spot after Kevin-Prince Boateng had collapsed to the turf following a collision with Nerazzurri goalkeeper Julio Cesar.
Replays should that Julio Cesar had clearly made contact with the ball before making any with the Milan trequartista, something that Rizzoli has know acknowledged.
"I was badly positioned," he told Sky Sport Italia. "The television images are indisputable: I made a mistake.
"If I had been in a different position I would have seen everything without any problem. It's a pity and I'm still sorry about the error."
While the penalty was converted by Zlatan Ibrahimovic, who then put the Rossoneri 2-1 shortly after the break, Inter actually went onto win the game 4-2, thus ending Milan's title challenge and handing the Scudetto to Juventus.