The chanting came from Lazio's North End and was also aimed at police who had clashed with fans on Wednesday at Piazza della Liberta in the capital when celebrations to mark the club's 119th anniversary turned violent.
Lazio dominated the last-16 tie against the Serie C side from northern Italy with Immobilie setting up Luis Alberto's 12th-minute opener for the Romans.
Novara goalkeeper Elia Benedettini saved Immobile's 20th-minute penalty, but the Lazio forward netted the rebound, adding a second 15 minutes later for his 13th goal in all competitions this season.
Serbian midfielder Sergej Milinkovic-Savic blasted in a free-kick to give the hosts a comfortable four-goal lead just before the break.
Umberto Eusepi pulled a goal back for Novara when he slotted in a penalty awarded for a Luiz Felipe handball after consultation with VAR just after half-time.
Lazio, who won the last of their six Coppa Italia trophies in 2013, will next play either Inter Milan or Benevento in the quarter-finals.
Juventus begin their quest for a fifth consecutive Coppa Italia later on Saturday at Bologna, as former five-time winners AC Milan are away to Sampdoria, who last won the Cup 25 years ago.
The Italian league is still on its winter break but Juventus and AC Milan are warming up for the Super Cup final in Saudi Arabia next Wednesday.