The Italian league's disciplinary tribunal said Lazio would have to stage one home game with part of the Olympic Stadium closed to fans if there was a repeat incident within the next year.
The tribunal said Milan's Tiemoue Bakayoko and Franck Kessie were subjected to racially insulting chants before and during Wednesday's match at San Siro from "almost all" of the 4,000 Lazio fans in the away end.
It said that the chanting could be heard "by everyone" in the stadium.
Lazio, who beat Milan 1-0 to qualify for the final against Atalanta, blamed "isolated elements" for the incidents.
However, Milan's sporting director Leonardo Araujo said after the game that it was "absurd" play had not been halted.
"There were one thousand reasons to stop the game," he told Gazzetta dello Sport.
"With the new rules, there is no need to wait for the second or third round of chants, the first is enough to take the teams to the middle of the pitch and make an announcement.
"In the case of more chanting, the match should be stopped indefinitely. But nothing happened. Everyone heard the racial insults and the monkey noises."
Before the match, a group of Lazio fans were photographed in the city centre displaying a banner which honoured Benito Mussolini.
(Writing by Brian Homewood; editing by Ken Ferris)
