Kevin De Bruyne and Giovanni Vergara, both introduced from the bench, scored either side of the hour mark to hand Allegri victory in his first competitive match in charge, though the win was overshadowed by Genoa's furious protests over a challenge by De Bruyne on Vásquez in the build-up to the opener.
De Rossi did not hold back when asked about the officiating afterwards.
"Let's move on, that's the only way we can deal with it. This time it's pretty clear — last year we waited for Open VAR to understand whether it was a penalty or not, it was a very different situation.
"This year I don't think there's a single person in the world who could think it wasn't a foul. I have a very positive view of the new refereeing setup, I spoke to Orsato before the match, and a very negative view of what happened tonight.
"This is one of the ugliest things that's happened to me since I've been involved in football. In my opinion Di Bello isn't a bad referee, but tonight's incident is different from all of that."
Despite his anger at the officiating, De Rossi felt his side's overall performance merited more.
"I'm happy with the first 55 minutes. We played a great defensive match and were very good with the ball. Their pride came out in the second half. For me it would have been a deserved draw — better us in the first half, better them in the second. We didn't concede many big chances against a strong side like Napoli and I think we deserved not to lose. We can improve on plenty of things, on consistency."
The Genoa coach also praised individual performances, singling out Morten Frendrup and Villum Ellertsson.
"Ellertsson is a priceless player, he keeps adding more and more quality. I like Frendrup a lot, when he raises his voice in training he does it with the big characters, he's not afraid, and everyone respects him for that. Frendrup wins the ball back when others would be tracking back."
Allegri, for his part, said his new side had needed time to settle into the contest.
"We had 25-30 minutes of difficulty because technically we misplaced a few passes. Genoa pressed well, they played a good match. Bit by bit the game came our way. Already in the first half we had two or three situations where we could have done better, and in the second half we took control of the game. For a first match I have to say the team played well."
The Napoli coach credited his bench for changing the course of the game, with both goals coming from substitutes.
"Substitutions become decisive because when they don't help the team, the team suffers through an important moment of the match, and tonight the players who came on did really well."
He was more cautious on Kevin De Bruyne's role from the bench, pointing to the Belgian's short pre-season.
"Kevin has been back with the team for barely 15 or 20 days, so maybe right now that's how it is, but in a month it'll be completely different once we're playing every three days."
Asked about the disputed opening goal, Allegri declined to weigh in.
"I've never commented on referees in twenty years, maybe once, because it's too easy to comment afterwards. What I can say is that Genoa played a good match — we knew this game would be difficult."