Rudi Garcia's side made it seven league wins in a row against Atalanta to keep the pressure on leaders Juve, who make the trip to Udinese on Monday.
And with the top two set to meet on May 9 at the Stadio Olimpico, Conte has refused to take anything for granted when it comes to securing a third straight Scudetto, along with a potential UEFA Europa League crown after the Italian champions moved into the semi-finals of that tournament last week.
"The title race is still open. I expected the head-to-head with Roma to go down to the wire," he said.
"It's been a hard season physically and mentally but we're still in the running on two fronts. We're living the moment.
"We've returned to our rightful position in the league and we're proud of that.
"Juggling two competitions? This is where we wanted to be. It's all good experience for me, the players and the club."
Juve's goals of late have come from various sources, with the likes of Andrea Pirlo, Carlos Tevez and Fernando Llorente all chipping in.
Pablo Daniel Osvaldo, who joined Juve on loan from Southampton in January, is yet to score in Serie A, but Conte backed the forward to find the net sooner rather than later.
"Osvaldo has come in here and worked his socks off. He'll help us achieve our targets this year," the 44-year-old added.
"Opposition teams pull out all the stops when they're up against Juve but we've come to expect that."
