The Belgian midfielder made his debut with the Giallorossi in Thursday's 1-0 triumph over Sampdoria in the Coppa Italia.
"I have immediately felt good," said Nainggolan, who joined Roma on loan from Cagliari this week.
"It's not easy to join a team that are doing great things.
"I still have to adapt to how the team plays but my first game has gone well.
"I have joined a strong team that has great players. I know there is a lot of competition to play but I'm convinced of my quality."
Thursday's result allowed Roma to bounce back from last weekend's 3-0 defeat against Serie A leaders Juventus, their next opponent in the quarter-finals of the Coppa Italia.
The reverse in Turin brought a shuddering halt to Roma's unbeaten run this season and saw the second-placed side fall eight points behind Juve and just two points clear of Napoli below them.
"Eight points is a lot," Nainggolan said. "It's clear that we cannot make any mistakes from here until the end of the season.
"But we will fight for the scudetto until there is no hope left."
Roma will be without defender Leandro Castan, midfielder Daniele De Rossi and striker Adem Ljajic, all serving a one-match ban this weekend.
Genoa travel to the Stadio Olimpico without the team's top scorer Alberto Gilardino.
The Italian striker, who has scored eight goals for Genoa this season, must serve a one-match ban.
"I'm really disappointed to miss the game at Roma," Gilardino said. "But I know we have good players like Emanuele Calaio that can do well in my absence."
Calaio, who has found the net just once in eight league games, will replace Gilardino in attack.
Genoa go into the fixture having halted a five-match winless run with a 2-0 victory over Sassuolo last weekend.
That victory was Genoa's first since November 10 and lifted Gian Piero Gasperini's side to ninth in Serie A.