Serie A's disciplinary tribunal said the Italian "made a derogatory remark to the fourth official when he was removed and then addressed the spectators with an insulting gesture".
Mancini was dismissed for dissent early in the second half as he protested against the referee's decision not to award a penalty to his side.
The Inter coach also used offensive language towards a television presenter during an interview after the match but that issue was not mentioned in the tribunal's report.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Writing by Brian Homewood; Editing by Tony Jimenez)
