Pochettino guided Tottenham to the 2019 Champions League final and turned them into Premier League contenders as they finished in the top four for four straight seasons before he was fired in 2019.
"Mauricio was an amazing manager for me. Great person, great, great coach. Helped me a lot to get to where I am now. So I'm really appreciative of him," Kane told Reuters.
The England captain was in New York this week to announce his investment in OxeFit, an AI-driven fitness-tech startup, joining ice hockey Hall of Famer Wayne Gretzky as a new partner with the company.
Pochettino, who has signed a two-year deal with the option of another year at Chelsea, takes over after a dismal season for the club in which they finished 12th in the Premier League, their worst finish since 1994.
"Everyone has their career, everyone has their future. So all I can say is I wish him all the best," said Kane. "I hope he does well - just obviously not as well as us."
Artificial intelligence could help reduce injuries, says Kane
Kane believes artificial intelligence (AI) could be the future of injury prevention in soccer as he bemoaned the fact that a number of leading players will miss this year's women's World Cup.
England won the women's European Championship on home soil last year but enter the tournament in Australia and New Zealand starting in July without stars including former captain Leah Williamson and 2021/22 women's player of the year Beth Mead.
Other major contenders including Olympic champions Canada and defending champions the United States will also be depleted.
"It's been a real shame to see some of the women players go down with those injuries and big injuries as well," Kane told Reuters.
While announcing his investment in OxeFit on Thursday, Kane said he is convinced in the power of real-time data to stop needless injuries.
"Injury prevention is something that is the most important thing to me," said Kane, who joins retired ice hockey Hall of Famer Wayne Gretzky among the latest investors in OxeFit.
"It (will) only get more impressive and more with AI will get better. And hopefully in the long run we'll start kind of seeing less and less injuries."
Kane pointed out OxeFit technology's ability to detect when an athlete might be favouring one side over another with real-time feedback.
"You've got a little issue on your left side or your right side and you need to even out because when you're playing game after game, all you're doing is just putting more impact on maybe the weaker side," he said.
There have been calls for greater research into the prevalence of injuries in the women's game and Kane, who helped England reach the World Cup quarter-finals last year, sees enormous potential in his country's women's team to move the sport forward.
FA chair Debbie Hewitt recently floated the idea of pursuing a bid to host the 2031 Women's World Cup.
"(We were) lucky enough we had the European Championship last year and I was able to go there, watch the final at Wembley, watch them win. And I saw how much it meant to the country - the country was so behind them, thousands and thousands of fans watching," Kane said.
"The European Championship is great, but the World Cup is the pinnacle of football."
