The 22-year-old was hit on the back and went down as he was being subbed prior to discarding the jug.
Mattia Zaccagni scored the main objective.
Lazio's Pedro and Roma's Sardar Azmoun were excused in injury time, with Gianluca Mancini, additionally of Roma, shipped off after the last whistle.
Zaccagni's champ was from a punishment granted by the video colleague ref for a foul by Dignitary Huijsen on Valentin Castellanos.
Roma supervisor Jose Mourinho has lost four of his six derbies since assuming responsibility in 2021.
"It's dependably difficult to lose, doubly so in the derby," he told Mediaset.
"It's a cutting edge football punishment, the sort that could not have possibly been given before VAR. The official didn't part with it when he was three meters yet with VAR he then gives it."
Lazio will play Juventus or Frosinone in the semi-finals.
In the interim, Atalanta beat AC Milan 2-1 because of two objectives from Teun Koopmeiners to set up a semi-last conflict with Fiorentina, who saw off Bologna 5-4 on punishments after a goalless draw on Tuesday.