The Portuguese, back in the game after 11 months out, led his new club to a 3-2 win at West Ham on Saturday -- their first Premier League away win since January.
Kane was a staunch supporter of Pochettino, crediting him with making him into one of the top strikers in the world, and visited the Argentine at his home after his dismissal.
"It's a week I've never really had in my career before," said the England captain.
"It was a big shock on Tuesday night for everyone, the players included, and then it was a quick turnaround.
"All of a sudden we've got a new manager, one of the best managers there's been in the game, so automatically you have to turn your head towards that and focus on the game."
Pochettino, who took Spurs to the Champions League final in June, ended his five-and-a-half year stint with no silverware.
Kane has expressed his desire to win trophies at Spurs and is hoping that Mourinho, a former boss of Chelsea and Manchester United, can help him achieve his goals.
"The gaffer's won at every club he's gone to -- there's no hiding away from that," Kane said.
"He wants to win. He's a proven winner. I've made it clear that I'm at the stage of my career where I want to win trophies.
"I've made it clear I want to win them here and it's a big year for us."
Kane said Mourinho's reputation for winning silverware gave the players confidence.
"It's almost a fresh slate for everyone now to show the manager what they can do and hopefully the players can thrive on that," he said.
Midfielder Eric Dier said the players were lucky to be able to work under Mourinho, whom he called the "perfect" replacement for Pochettino.
"His record is unbelievable and he transmits that confidence. The way he speaks, you believe it, you feel it from him," Dier said.