The reigning Serie A champions moved 17 points clear of the second-placed Roma after Andrea Pirlo curled in a superb free-kick in the 89th minute.
Pablo Daniel Osvaldo had two first-half goals ruled out for offside and Genoa had the chance to take the lead after Arturo Vidal conceded a penalty for handball.
Substitute Emanuele Calaio had his weak spot-kick comfortably saved by Gianluigi Buffon though, before Pirlo sealed victory for his side.
Conte told Sky Sport Italia: "Inevitably coming here and winning in Genoa against a team that played the game of their lives, after our run of matches with tired players I couldn't rotate, it means only a great team could've done it.
"There were also some controversial incidents, but we know referees are humans and can make mistakes, so I compliment the officials.
"Genoa were very aggressive, but the forwards did very well to hold on to the ball and we had scored other goals, so I am satisfied. We could've been more precise in the final ball, but they did well both attacking and defending.
"This team is having a super-fantastic campaign and at the end of the day people have to admit it, even if they do so with a heavy heart.
"I hope to win the Scudetto (Serie A), then it will be in the record books and the chatter will be gone with the wind."
Pirlo added: "We knew it would be a difficult game. It was an important goal that we hope will be helpful in winning the Scudetto."
Buffon hailed the efforts of Pirlo and said: "There's always hope when Pirlo has the ball at his feet. He's one of those players who allows you to dream."
Genoa manager Gian Piero Gasperini said losing to a late goal was unfortunate for his team.
"Losing a game like this is incredibly painful," Gasperini said.
"We played well for 90 minutes and we thought that we'd be able to win it and make history, so to lose is hard to swallow.
"Considering the quality of our opponents, it was undoubtedly our best performance of the season.
"It's a real shame, as we had the game in (our) hand during the second half and had that penalty.
"I can only compliment my players. It’ll be tough to raise their spirits, but they must remember the performance."
