The victory could mark the final Milan game of the Silvio Berlusconi era, with the club due to be sold this week.
Galliani reflected: "In 31 years we have brought AC Milan at the top of the world.
"If we will change ownership, we will remember everything we've done. Tomorrow I'll be at lunch by the president.
"I am very happy for today."
He also said: "Today we did well. I heard from the President, if this was our last game it was a beautiful game that will remain in our minds and in those of the fans."