Liverpool returned to winning ways in the Premier League with a 4-1 hammering of City at the Etihad Stadium.
Brazil international attacker Firmino was on target for the Reds just past the half-hour mark.
Former United defender Neville was impressed with Liverpool’s performance and claimed that Firmino could have scored four goals.
“Liverpool were so good," the former England international told Sky Sports. "When teams give you chances, there's still a lot to do.
“Obviously, the [Eliaquim] Mangala own goal was a bit of good fortune but the Firmino pass for Coutinho's goal was sensational.
“Then the little favour returned on the one where Coutinho reversed it back to him. It's not easy to do that. It's hard to play that pass when your eyes open up and the goal is there.
"How many times do we see players shoot in that position and we say, 'Why didn't he pass there?' Liverpool, it seemed, played the right pass so many times in the final third. Firmino could have had three or four goals.”
Firmino, who joined Liverpool from German outfit 1899 Hoffenheim in the summer transfer window, had a good game against City.
The former Figueirense man took five shots, had a pass accuracy of 70%, created two chances, attempted four dribbles, and made one clearance.
Liverpool are ninth in the Premier League table at the moment with 20 points from 13 matches, six points behind fourth-place Arsenal.