Pochettino began his news conference ahead of Tottenham's Champions League last 16 second leg clash against Juventus with a moving tribute to the 31-year-old defender.
"I want to send all my condolences to Davide Astori and all the people that love him and I think it's a massive tragedy," Pochettino told reporters.
"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 on Saturday, 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."
Pochettino has first-hand experience of a similarly tragic event. He was manager of La Liga side Espanyol when his player Dani Jarque died during pre-season training in Florence.
"I know it's so difficult, it's impossible to take away that pain and find an explanation," he said.
"It's so difficult, it's so difficult to understand what happens in these type of things."
Astori was found dead in his hotel room on Sunday in Udine where Fiorentina had been due to play Udinese in the league. All of Sunday's Serie A matches were postponed.
There will be a minute's silence in tribute to Astori before kickoff at Wembley on Wednesday, as there will be in all this week's Champions League and Europa League fixtures.
(Reporting by Martyn Herman; Editing by Christian Radnedge)
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