Lazio were embroiled in controversy on Saturday after racist and anti-Semitic chanting which scarred a Coppa Italia tie was dismissed by the club as a "psychosis focusing on a minority or non-existent incidents".
Lazio crushed third-division Novara 4-1 in their last-16 game at Rome's Stadio Olimpico.
However, their hardcore ultra fans aimed a series of ugly barbs at the club's bitter city rivals Roma, with taunts of "Yellow, red and Jewish" and "This Roma that looks like Africa".
They also targeted police who clashed with Lazio fans on Wednesday at Piazza della Liberta in the capital when celebrations to mark the club's 119th anniversary turned violent.
Eight police officers were injured and four supporters arrested.
Lazio spokesman Arturo Diaconale blasted reports of the chanting by a small section of the crowd as "a psychosis".
"I am one of the 98 percent of people in the stadium who didn't hear them," he said.
"The club naturally condemns any racist or anti-Semitic chants .. I think it's a form of psychosis focusing on either a minority or non-existent incidents."
On the pitch, Ciro Immobile scored a first-half double, after Luis Alberto's 12th-minute opener with Sergej Milinkovic-Savic claiming the fourth before the break.
Umberto Eusepi pulled a goal back for Novara, a third-tier side based 50km west of Milan, from the penalty spot just after the break.
Holders Juventus booked their ticket to the quarter-finals with a 2-0 win at Bologna, with AC Milan going through by the same scoreline after extra time against Sampdoria.
Juventus and AC Milan will meet in the Italian Super Cup final in Saudi Arabia next Wednesday.
Cristiano Ronaldo and Paulo Dybala started on the bench for the champions with a view to the game in Jeddah.
Juventus eased through with Federico Bernardeschi opening the scoring after nine minutes and Moise Kean adding the second four minutes after the break.
In Genoa, Brazilian international Lucas Paqueta started for Milan after his arrival from Flamengo in a 35-million-euro ($40 million) deal last week, along with want-away Argentine Gonzalo Higuain amid speculation he is about to move to Chelsea.
Higuain thought he had scored but was ruled offside.
Patrick Cutrone came on as a substitute in extra time with his two superb volleys on 102 and 108 minutes setting up a meeting for last year's finalists with either Napoli or Sassuolo.
"We need to regain our energy. It will be a big match and one that can help us with our character, it could be a turning point for us," said AC Milan coach Gennaro Gattuso of next Wednesday's game.
Napoli host Sassuolo on Sunday while Inter Milan play Benevento in a closed San Siro as punishment for racist chanting against Napoli's Franco-Senegalese defender Kalidou Koulibaly in a Serie A game on December 26.
Roma entertain third-division Virtus Entrella at the Stadio Olimpico on Monday.