The Italian side crushed Valencia 4-1 on Wednesday to take a giant step closer to reaching the Champions League quarter-finals for the first time.
Dutch wing-back Hans Hateboer scored twice on 16 and 62 minutes, sandwiching goals from Josip Ilicic and Remo Freuler.
"This is an evening that we'll remember forever," said Gasperini. "It's an amazing result, full of emotion."
It was an extraordinary night for the side from Bergamo who travelled to the San Siro with over 40,000 of their fans as their home stadium 55km away does not meet UEFA regulations.
Denis Cheryshev pulled one back for Valencia.
Valencia, seventh in La Liga, had finished top of their group after away wins over Ajax and Chelsea but were missing several key players through injury and suspension.
"It certainly complicates things a bit, it's a pretty overwhelming result, this 4-1," said Valencia coach Albert Celades.