The Swede, 21, arrived at Spurs on deadline day on an initial loan from Juventus and made his debut in the 3-1 FA Cup fourth round victory over Brighton.
The striker says the experience he got working under Italy legend Pirlo in Turin should stand him in good stead as he looks to supply striker Kane.
"Pirlo is a fantastic coach and a fantastic guy," he said. "I spoke with him nearly every day and he always spoke to me a lot about how I should shape my body and how I can look for passes without showing the opposition where I am going to play the ball.
"And that is exactly what I hope will help me to help Harry even more in the future.
"He (Harry) is unbelievable. Yes, up there. What impressed me was his technique, the way he stopped the ball and the way he changes the whole pitch with his passes from both feet.
"It is amazing really. And I know that when he has the ball I have to run because he will find me."
Kulusevski was joined at Spurs by his Juve team-mate Rodrigo Bentancur and he also put in an impressive cameo in the middle of the park.
Boss Antonio Conte said it was important both men got a taste of English football.
"It was important also to breathe the atmosphere for the two new signings, for us, for Dejan Kulusevski and Rodrigo Bentancur," he said.
"It was important to come in and to understand the intensity of this league. I repeat, two good players, two young players with talent. They can help us.
"Rodrigo, despite his age, only 24 years old, has a lot of experience because he played 120 games for Juventus. Kulusevski, the same. I think they can help us.
"I'm pleased that I gave them the opportunity to come in and also breathe this fantastic atmosphere in our stadium. Our fans, the noise tonight was so intense that it was also very difficult to communicate with the players."
Brighton briefly threatened to get back into the cup tie at Spurs after Kane's strike and a Solly March own goal but the hosts were in command when Yves Bissouma scored a deflected effort from the edge of the area.
Bissouma, who was linked to a January move away from Albion, was playing his first game back since returning from international duty with Mali.
"He is an important player for us and he looked like he was enjoying his football," boss Graham Potter said.
"He grew into the game. In the second half he had a lot of impressive actions, you can see his quality.
"He hasn't had much training with us, just a couple of days, but we know his quality, we know what he can do, so I'm really pleased that he got a goal."