Antonio Conte was left fuming over a heated post-match exchange with Juventus chairman Andrea Agnelli following Inter's Coppa Italia semi-final exit.

The Milan-based side were held to a tense 0-0 draw in the second leg at the Allianz Stadium as the Old Lady advanced to the final, 2-1 on aggregate, before ugly scenes allegedly erupted following the final whistle.

Media outlet RAI reported that Conte made an insulting gesture towards his former employer Agnelli at half-time, and the Juve chief retaliated by verbally abusing the Inter coach as the teams left the field.

Conte criticised his former club's behaviour in his post-match interview but stopped short of pointing any fingers.

"Juventus should tell the truth," Conte told RAI. 

"I think the fourth official heard and saw what happened throughout the match.

"They should be more polite in my opinion. They need more sportsmanship and respect for those who work."

Conte coached in Turin between 2011 and 2014 and led the Bianconeri to three Serie A titles before taking up a role in charge of Italy after the 2014 World Cup.

The 51-year-old was questioned on the incident in his post-match news conference but he refused to elaborate.

"What happened at the end of the game? I have neither the desire nor the pleasure to comment on anything," Conte said.

"I think that in all things there must be education. Enough."

The competition's most successful club, Juventus, advance to the final to face Atalanta or Napoli, as Andrea Pirlo's side search for a 14th Coppa Italia triumph.