Stephan El Shaarawy and Artem Dovbyk, along with an own goal, struck for Roma. Patrizio Masini also netted for the visitors.
Afterwards, Ranieri beamed: “It was a tough game, because Genoa have really become solid since Patrick Vieira took over and it was difficult to find a way through, especially after we conceded from a set play.
“We persevered, it was tough, but we wanted it to thank these 62,000 fans who came here on a Friday night to cheer us on. I assumed it’d be 30,000 and it was double that. We must do everything for these people, because they love us beyond every limit. When they protested, it was because extreme love makes them always want the maximum.
“I tell the players to give their maximum, because even if we don’t get the result, I at least know they’ve given their all and that is the most important thing for me.
“Seeing how they all train is marvellous, as we play every three days and so we need everyone. El Shaarawy is one of the most experienced players in the squad and I know that I can always count on him."