The former Argentina international's stock rose markedly during his 16 months at Saints, who he led to their best-ever Barclays Premier League finish last season.
However, after months of speculation, Pochettino this week signed a five-year deal to become head coach at Spurs, taking his backroom staff with him.
The move raises questions over Saints' future direction and has disappointed midfielder Wanyama, who moved to St Mary's last summer from Celtic in a £12.5million deal.
"I learnt a lot from him, he taught me more and that's why I have grown as a player and there is a big difference compared to when I was at Celtic," Wanyama said. "He played a big role in my career development.
"I wanted him to remain because he had the passion for the club and I think the owners should not have let him go because the team can do better next season.
"It's a big blow because he had good connection with the players."
Pochettino's exit raises questions over the future of Southampton's players, such as Luke Shaw and Adam Lallana - players Wanyama hopes stay as they "can build a successful team together at Southampton".
Teenager Shaw is currently away with England's World Cup squad and took to Twitter to thank the departing Saints manager.
"Would like to thank Mauricio for everything he has done for me," the 18-year-old said. "Great manager, great guy and has helped me a lot. Wish him all the best."