Pochettino has suffered tragedy before when manager of Espanyol when one of his players, Dani Jarque, died while on pre-season training in Florence and he also knew Astori from nearly signing him five years ago.
Pochettino said: “First of all, I want to send all my condolences to David Astori and all the people that love him and I think it's a massive tragedy.
“I had the possibility to meet him five years ago because it was my idea to sign him when we were at Southampton. I took three hours to have lunch with him and he was a great kid, great person, great professional, great player.
“It was very sad news, devastated to hear the news and we share the pain with all the people in Italy and Florence and I send all my energy to his family.
“Yes, for me, it was like, for everyone, it repeated everything in my mind with what happened in Florence, with what happened with Dani when I was manager of Espanyol.
“I know it's so difficult, it's impossible to take away that pain and find an explanation. It's so difficult, it's so difficult to understand what happens in these type of things."