Conte, who selected Astori during his reign as Italy coach from 2014 to 2016, was visibly distressed when he spoke about his former player.
Conte told Sky Sports: "This is a tragedy and it really hurts me. It's very difficult at this moment to find the right words for the family.
"I had him with the national team. He was a great player but especially a fantastic guy. I stay close to his wife, parents and daughter. He was only 31 and it's very difficult to explain this situation."