The Bianconeri – who have already been fined for similar incidents this season – were punished relatively leniently for their cooperation with the authorities and positive steps to eliminate crowd trouble from the stands.
It was not specified who the chants were made against, but Milan had several black players on the field that night, including Sulley Muntari, Clarence Seedorf and Urby Emanuelson.
Juve are reported to have passed details of offending supporters to the police, and have vowed ban anyone found guilty of disorder.
They have also worked to restrict entry into the new Juventus Stadium using heavy security to prevent fans bringing offensive banners or dangerous objects to matches.
Italy has a long-standing problem with hooliganism and racism at football matches, but Juventus have been working to create an English-style ‘safe’ stadium at their new ground.
They have struggled to change the attitudes of some supporters though: the club was fined 10,000 euros after fans chanted racist slogans at an Internazionale player earlier this season, while they were repeatedly censured for abuse of Italy striker Mario Balotelli when he played for Inter.
Juve won Tuesday’s match thanks to an extra-time strike from Mirko Vucinic, making it 2-2 on the night and 4-3 on aggregate.