Gazzetta dello Sport published a video clip of Lazio fans chanting insults about Milan midfielder Tiemoue Bakayoko outside San Siro ahead of the game on Wednesday evening.
The same insults were also heard inside the ground as the teams were warming up, the newspaper and other Italian media reported.
Earlier, a group of fans were photographed unveiling a banner that read 'Honour to Benito Mussolini' in the city centre.
"Lazio takes clear distances from behaviour and events that do not reflect in any way the sporting values sustained and promoted by the club for 119 years," the club said in a statement.
"And it rejects and disputes the simplistic tendency of some media to consider the entire Lazio support jointly responsible for acts carried out by a few and isolated elements, for reasons foreign to any form of sporting passion."
Italian football has been plagued by incidents of racism over the last few years.
Inter Milan were ordered to play two matches behind closed doors after Napoli defender Kalidou Koulibaly was subjected to racist insults during a match at San Siro in December.
Juventus teenage forward Moise Kean was also the target of alleged racist abuse during his team's 1-0 win at Cagliari earlier this month. Serie A are still investigating the incident.
Lazio won the semi-final second leg match 1-0 and will meet either Atalanta or Fiorentina in the Coppa Italia final in Rome.
(Writing by Brian Homewood)
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