Pochettino resigned from his position at Southampton on Tuesday, moving to White Hart Lane on a five-year-deal.
The Argentinian brought Wanyama to St Mary's from Celtic last July for a fee believed to be in the region of £12.5 million.
And the Kenyan was quick to express his dissatisfaction at seeing the 42-year-old leave Southampton.
"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 told Capital FM Kenya.
"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."
There has been speculation that left-back Luke Shaw and attacking midfielder Adam Lallana may follow Pochettino out of Southampton.
However, Wanyama is keen for the club to avoid further departures.
He added: "I don't want the pair to leave since we can build a successful team together at Southampton."
