Richarlison caught the eye with an all-action display on his full debut and set up Pierre-Emile Hojbjerg's opening goal before hitting the post and seeing a late strike ruled out for offside.
The £60million signing from Everton replaced Dejan Kulusevski in Spurs' front three and linked up well with Kane, who scored the second goal, and Heung-min Son.
"He was brilliant," said Kane, who moved level with Thierry Henry as the top scorer in Premier League London derbies, with 43.
"He has been doing great every time he came off the bench. He was ready once he started [a game] to make a real impact, and from start to finish he was fighting for every ball, making good runs and getting chances and unlucky not to score with the offside and one off the post.
"Brilliant to have him and he has to keep doing what he has been going and help the team as much as possible.
"He has got that mindset where every tackle and every training session he just wants to play football and impress the manager.
“He has definitely been doing that and he has been a great addition to the team, he needs to keep working hard.
"He came in for Kulu and they are different players as they play with different feet. Kulu likes to maybe come inside more and make crosses with his left and Richy I felt was maybe playing closer to me as a striker and linking up and making runs down the middle of the pitch.
“Whoever plays we have to make a good connection and I thought we did that on Saturday."
Spurs will play their first Champions League game since March 2020 on Wednesday night when they host Ligue 1 side Marseille in their opening group game.
Kane is excited to be back in the competition following a season each in the Europa League and Europa Conference League.
"I'm really excited," Kane said. "It was a great finish to last season to get that spot. It has been a few years since we were in it and we missed it as players and the club.
“At home under the lights the crowd will be really excited. We need to start well it is an important competition for us. We feel like we can go well so we need to go and win.
"It is part of every player’s career that sometimes you go through stages where you can’t play at the top level where you want to do and that is where we have been at for the past couple of years.
“When you are watching the Champions League it is where you want to be and the nights you want. It has been a while and we are itching to start the competition well.
“I am looking for it and as a player I want to be playing in the biggest competitions.”
Spurs avoided the big guns from Pot 1 in the draw but also face Europa League winners Eintracht Frankfurt and Sporting Lisbon.
“In the Champions League, you can always have a difficult game, we will take the draw,” Kane added.
“Three good teams and on their day they can be good as anyone. And we are not taking it for granted. We need to make sure we play every game well and the away game will be especially tough. Every game we play away will be difficult so it is important to get off to a good start at home.
"I don’t know too much about Marseille. We have a day off Sunday so on Monday we will start to analyse them, their threats and we need to try to put our stamp on the game. We will do tactical [work] for sure leading up to it and try to learn as much as we can in that short time."