The leader of Serie A's governing body has called for an end to the criticism of the decisions made following the recent Scommessopoli trials
Conte, who became embroiled in the recent match-fixing investigations during his time at Siena, has been been given a 10-month suspension from the dugout on match days, although he is still allowed to oversee day-to-day training.
The Serie A champions have taken a firm stand against the allegations directed at their manager, and Abete has now issued a plea for calm, and is adamant that the FIGC are merely doing their job.
"The sporting justice system is autonomous and must perform its role," Abete told Sky Sport Italia. "Juventus are a great club, although our relationship with them has been strained of late."
Controversy surrounding the issue took another twist when Roma coach Zdenek Zeman recently insisted the former Bianconeri midfielder should be banned from training as well.
"It is better not to speak about an issue when not directly involved in it. The way things work now, a banned coach is still permitted to train the team normally.
"Italian football, earnestly, has to work on improving its behaviour. Napoli [after they boycotted the Supercoppa Italiana prize presentation] ought to learn how to differentiate between respecting the success of their opponents and exhibiting their criticism so brazenly."
Napoli were dragged into the argument after the Partenopei's 4-2 loss to Juventus in the Italian Supercoppa final, following which the club then deliberately missed the trophy presentation in protest to decisions made by the match officials.