Chiellini, who is releasing a new book, accused Mario Balotelli of being "a negative person" who "deserved a slap" for his conduct when part of Italy's squad at the 2013 Confederations Cup.
The Juventus defender was even more brutal when it came to his ex-club team-mate Felipe Melo, calling him "the worst of the worst" and revealing he told the team's management the midfielder was "a rotten apple".
Both players promptly hit back at Chiellini, who also expressed his hatred for rivals Inter. Balotelli insisted he had never disrespected the Italy shirt and slammed the Juve man for not telling him to his face, while Melo branded the veteran "unprofessional".
Tardelli spent 10 seasons with Juve and then two with Inter to conclude his Serie A career, while he won the World Cup with Italy in 1982.
He reacted to Chiellini's words on Twitter, posting: "I am truly disappointed by the statements by Giorgio Chiellini, captain of the national team, Juventus and a leading man on the AIC [Italian Footballers' Association] board.
"Harsh words towards team-mates - colleagues who should consider him a point of reference.
"The hatred declared towards another club creates hatred. Respect for the opponent even in the toughest fight, that is what I learned from captains like Dino Zoff and Gaetano Scirea."