It is claimed the two Milan midfielders were subjected to monkey chants during the game at San Siro, which the visitors won 1-0.
There were also reports of inflatable bananas being held up in the away section, while a group of ultras are said to have erected a banner in the streets in the hours before the match praising former facist dictator Benito Mussolini.
In a statement released on Thursday, the club said: "AC Milan wants to reiterate its condemnation of all forms of racism and discrimination following the incidents of last night's Coppa Italia semi-final second leg game between AC Milan and SS Lazio.
"Recurring chants and monkey noises directed to players Franck Kessie and Tiemoue Bakayoko could be heard coming from the away stand before, during and after the match.
"Throughout their 120 years of history, the Rossoneri have always honoured the values of sport, respect and inclusion, which underpin everything we do.
Ancora una volta uniti contro il razzismo— AC Milan (@acmilan) April 25, 2019
Once again, united against racism pic.twitter.com/nkgCuv99QZ
"The club wants to thank all players from both teams for their professionalism and their fairness, as well as its fans for their passionate support and their responsible behaviour despite a climate exacerbated by unacceptable episodes.
"AC Milan has felt an obligation to report yesterday's serious incidents to the highest sports governing bodies, with the hope that, with everyone's commitment, measures are implemented to eliminate racism from all stadia."
AC Milan executive chairman Paolo Scaroni added: "It was disheartening to watch such an important sporting event in our stadium, whilst monkey noises and racist insults were coming from the stands. We must be extremely vigilant.
"Football is respect. Football should not divide but unite people."
Lazio moved to distance themselves from any such incidents on Wednesday but also criticised sections of the media for "simplistic" reporting in which they "consider the entire Lazio supporter base jointly responsible for acts carried out by a few".
That incident came after Bakayoko, on loan from Chelsea, appeared to take exception to Acerbi's claims in a pre-match interview that there was "no comparison" between the quality of the teams.