Juve coach Conte reacted furiously to referee Marco Guida's decision not to award the Bianconeri a stoppage-time penalty for a perceived handball by Genoa defender Andreas Granqvist, while Chiellini - currently out through injury - stormed onto the pitch and remonstrated with the official after the final whistle.
They, along with Leonardo Bonucci and director Beppe Marotta, received bans for those actions with the Lega Calcio maintaining that a handball, such as the one in this instance, would not be ruled an infringement as it took a deflection before striking the player's hand. The matter was discussed on Monday at a meeting between referees, Serie A coaches and club captains.
President of the Italian referee's association Stefano Braschi, discussing the Granqvist incident, said Guida was right to interpret the incident as he did.
"It was a complicated situation," Braschi said. "We spoke about it today and almost everyone said the handball was not intentional. The fact that Granqvist basically kicked the ball at his own arm was evaluated. Almost everyone agreed with that. Guida noted what occurred with certainty. In cases like this it was right to not award a penalty."
Conte, who was present at the meeting, accepted the explanation and duly apologised for his reaction to the case.
"He understood that he went a bit too far," Braschi continued. "What counts in situations like this is whether the handball is voluntary or not."
Bonucci apologised last week and, on Wednesday evening, fellow Italy international Chiellini followed suit.
"Now that the controversy about that match has gone, I would like to apologise publicly for the incident," he said in a statement on his personal website. "Unfortunately, watching the game from the stands gave me more tension and after the end of the match I reacted too vehemently.
"We players should be the first to give a good example of how to behave on and off the field, so I wanted to apologise to all football and sports fans in general for my behaviour."