The 67-year-old coach claimed earlier in the week that Serie A is too easy for the Bianconeri and also questioned the current manager's reaction to last week's draw at Verona
Earlier this week, the 67-year-old former Bianconeri boss claimed that the club's exit at the group stage of this year's Champions League was down to the fact that Serie A is now too easy for them.
Capello also criticised Conte for taking away the current squad's day off last Monday in response to the concession of a late equaliser against Verona the day before.
“When a guru of football speaks, we ought to just kneel down and say, ‘Yes, sir!'” the former Italy international sarcastically stated in an interview with Rai Sport.
“Capello talked about a lot of things. In his view we are playing an amateur tournament. Since I’ve been here he likes to talk about Juventus a lot and stick his nose in. Perhaps our statistics and records annoy him.
“Other historic coaches of Juventus, like Marcello Lippi and Giovanni Trapattoni, are respectful and Capello is not.
“He ought to focus more on trying to get Russia past the first round at the World Cup. If I were in his position, I wouldn’t have said anything. Who is Capello to say if I did something wrong?”
Conte spoke just as scathingly about Capello's Juve tenure in an interview with Sky Sport Italia, bringing 'Calciopoli' in to the argument as the refereeing scandal resulted in the Bianconeri being stripped of two titles.
"I’d say someone who makes these comments is annoying and disrespectful to record-breaking campaigns over two years,” the former midfield ace fumed.
"I don’t like people who try to act like teachers when they don’t know the situation and frankly ought to look into their own houses, as there’s probably more stink there.
"Maybe someone is annoyed that our numbers could surpass those of that Juventus [of a decade ago], who won two Scudetti but not with a memorable style of play.
"I remember the Juventus of [Marcello] Lippi, of [Giovanni] Trapattoni. I only remember that Capello's Juve won two titles that were revoked."
Conte also defended his decision to make his players train on Monday.
"At times I have to raise my voice so we do not lose sight of the road that we're on.
"I didn't do it because we drew in Verona but rather because of the way it happened.
"It was right to do it to ensure that we continue to grow further. It was done to point out that we should not be dropping certain points on the road."
Conte then directed his fury at those among the Juventus Stadium crowd who booed Sebastian Giovinco during Sunday's 3-1 win over Chievo.
"I find the atmosphere that has been created around him unfair," he told Sky Sport Italia. "I cannot explain it.
"There is such bitterness that I do not even want to talk about it. Everyone should examine their conscience."