Having overcome Udinese 1-0 this weekend, the Nerazzurri have now won three out of three games in the league and moved to the top of the table, where they sit two points ahead of Juve.
Conte, however, warned his players to block out premature thoughts of a title tilt as they seek to end the hegemony of the Turin giants and clinch their first Scudetto since 2010.
"We are growing and I'm happy about our maturation," Conte said.
"But I also know that now you talk about us so you can beat us when something goes wrong.
"Today we talk about Inter as Juventus' main rivals. I know the game and it is what it is.
"But we have to keep our feet on the ground. Let others talk, we must shut up and work."
While Inter secured victory on Saturday, Juventus could only pick up a point against Fiorentina and Conte's counterpart Maurizio Sarri was unhappy with having to play in the afternoon.
The Serie A champions lost Douglas Costa and Miralem Pjanic to suspected muscle problems amid high temperatures in Florence as the game finished 0-0.
Sarri, who took to the touchline for the first time since a bout of pneumonia, partly attributed the frustrating result to the energy sapping conditions and suggested a later kick-off would have made a difference.
But his fellow former Chelsea boss believes the Bianconeri can have no excuses for not performing.
"I won't say anything because otherwise I would have to bring out the budgets, the turnover and the balance sheets," said Conte, who spent three seasons in charge of Juve.
"I will only say that someone now on the side of the strongest team should be calm and comfortable."