First-half goals from Arturo Vidal and Carlos Tevez temporarily brought reigning champions Juve within two points of the Giallorossi, who were struggling to break Udinese down at the Stadio Friuli.
By the time the final whistle blew at the Juventus Stadium, however, Conte had learned of Michael Bradley's winning goal in the north east, a strike which kept Roma perfect with nine wins from nine and five points out in front.
Napoli are joint second with the Bianconeri following their 2-0 win over Torino.
Conte could, however, take comfort from an attacking display which eased the disappointment of last week's defeats to Fiorentina and Real Madrid.
He told juventus.com: "It was a good performance, as we also saw in parts of our games in Florence and Madrid.
"The difference this time around was that we got what we deserved. We played with a good attitude, vital when facing a competent side like Genoa.
"We dominated proceedings and could have even scored more and, for once, we managed to keep a clean sheet."
The Juve boss would not leave the press conference without complimenting his Roma counterpart Rudi Garcia.
He added: "I can only take my hat off to Roma. Their winning run is overshadowing anything good that ourselves and Napoli are producing."
Genoa boss Gian Piero Gasperini, meanwhile, had rookie goalkeeper Mattia Perin to thank for keeping the scoreline respectable, with the 20-year-old consistently denying Tevez and his marauding strike partner Fernando Llorente.
The game appeared to finally turn in Juve's favour when Vidal converted the penalty won for Davide Biondini's foul on Kwadwo Asamoah, which was a marginal call given it occured on the very edge of the Genoa box.
Gasperini played down the effect of the spot-kick on the overall dynamic of the match.
"You really need a bit more evidence to give a penalty, but that's not what changed the game," he told La Repubblica.
"If it hadn't been for Perin that we would have already been a long way behind in the first half.
"Defeats are never easy to swallow but the strength of Juventus helped us better identify our weaknesses."
A fifth defeat of the new season leaves Genoa 16th in the table, two points clear of the relegation places.