Capello, who now coaches Russia, questioned Juve's ability to succeed in Europe in midweek, insisting that the Italian top-flight was not competitive enough to prepare them for the UEFA Champions League.
Juventus have won the last two Serie A titles and sit comfortably clear of Roma in their bid for a third – but failed to make it out of the Champions League's group stages this season.
Conte was unhappy with Capello's comments though, responding after goals from Kwadwo Asamoah, Claudio Marchisio and Fernando Llorente helped them continue their perfect home record in this season's Serie A.
"Maybe next year I'll ask us to be enrolled in the Premier League," Conte told Sky Sport Italia.
"I'd say someone who makes these comments is annoying and disrespectful to record-breaking campaigns over two years.
"Capello's sides broke record and their two titles were revoked (due to the Calciopoli scandal), but I don't remember their style of football.
"I remember Marcello Lippi's team and even Giovanni Trapattoni's, as they played well, but Capero's era is famous only for the revocation.
"I think this Juventus is more complete in every area than my first season. We were on a charge the first time and were the only side to stop Zlatan Ibrahimovic's Milan winning the Scudetto.
"This is the third season and in my view we have improved in every respect: tactically, physically and psychologically."
The win marked Conte's 100th Serie A match in charge of Juventus in style, with 70 of them ending in victory.
He said the result was important – despite admitting his side were not at their best throughout the contest.
"It is difficult to keep the same intensity for 95 minutes. At the moment we can't afford not to, as the moment we drop the concentration levels by a millimetre anything could happen," he said.
"Chievo scored with their first chance, which to be honest we scored ourselves (Chievo benefited from an own goal).
"There are moments in a season when any shot can turn into a goal, so you've got to watch out with Roma and Napoli coming up behind you."
