Conte, who became embroiled in the recent match-fixing investigations during his time at Siena, has 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 Sports.
"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 Juventus 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," Abete said.
"Italian football, earnestly, has to work on improving its behaviour. Napoli (after they boycotted the Supercoppa trophy presentation) ought to learn how to differentiate between respecting the success of their opponents and exhibiting their criticism so brazenly."