Mancini, who claimed Sarri hurled homophobic insults at him, has been fined £3,800 for his part in a spat between the two on the touchline during Tuesday night’s quarter-final, which Inter won 2-0.
Both men were found guilty by Serie A for insulting the fourth official.
Tempers boiled over between the two benches when Inter secured the victory in injury time and Mancini was eventually sent to the stands.
The former Manchester City manager claimed in a post-match television interview with Rai Sport that Sarri had used unacceptable, offensive language during their confrontation.
“You have to ask Sarri what happened. Men like him shouldn’t be in the world of football. He is 60 years old and must be ashamed,” said Mancini, who claimed to have been subjected to two homophobic phrases.
“The fourth official heard everything, but didn’t say a word, and I was sent off. This incident overshadows the rest of the match and is an embarrassment.
“He tried to find me after the match and asked for forgiveness, but he should be embarrassed. In England, someone like him wouldn’t even be allowed on a training pitch.”