Agroppi, himself a former Italy international and Serie A midfielder, is known for his outspoken manner and did not pull any punches with his opinions on multiple league winner Conte.
Conte is famously strict as a coach, even down to players' diets and use of free time. His playing systems require abnormally high work-rate and tactical rigidity from the entire team, and he is explosively animated during matches.
“I don’t like Conte because of his exhibitionism - too much shouting and drama on the sideline," Agroppi said to TMW Radio in Italy.
"You don’t win by putting on a circus act and howling.
“He always had great teams, but also suffered heavy defeats. When I hear talk that he brought a strong mentality to the Italy squad [he was coach for the Euro 2016 campaign], I find it laughable.
"Conte is just playing a part - it suits him when he wins, but when he loses, he becomes unbearable for players and directors. Don’t forget, that Italy didn’t even get into the top four at the Euros.
“Conte is overrated, as once again this season he crashed out of the Champions League in the first round with Inter and is falling behind in Serie A.
"He was fired by Arezzo and Atalanta. He won the Scudetto with Juventus, as did many others, but never made an impact in the Champions League.
"I wouldn’t mind if he wasn’t so over-the-top, with his commands and screaming. That’s only acceptable as long as you’re winning, otherwise you become irritating.”
Agroppi was asked if Conte's current high-flying Serie A rival coaches, Lazio's Simone Inzaghi and Maurizio Sarri of Juventus, had better managerial styles.
“Inzaghi doesn’t even look like a coach, he is everyone’s big brother or best friend. A coach must not be friends with his players.
"Your squad ought to be afraid of you and respect you at the same time, so you don’t lose your power.
“Sarri is either loved or hated depending on his latest result. If he only wins the Scudetto this season, what has he really achieved?”
Conte won Serie B with Bari, three consecutive Serie A titles with Juventus, the Premier League and FA Cup with Chelsea, and took Italy to the quarter-finals of Euro 2016 where they lost via penalty shootout to Germany after knocking out defending champs Spain in the round of 16.