The England captain scored twice as Spurs beat Arsenal 3-0 to move one point behind their rivals in the race for Champions League qualification but says the victory will count for nothing if they slip up against Burnley this weekend.
Kane said: "We need to win, otherwise it makes their job a lot easier. So if we can do that, it makes their game a lot tougher at Newcastle. We’ll be watching it for sure, [but] I don’t know if I’ll have the popcorn out."
The forward has urged Spurs to start fast if they are to overcome the Clarets and knows it will be a difficult challenge with their opponents battling against relegation.
He said: “You saw tonight, and against Liverpool, we had really high energy without the ball, with the ball, and created chances, and obviously scored some goals.
"So when you’re playing teams like Burnley at home, especially when there’s pressure on the game, you have to keep the energy high.
"Burnley are fighting for points themselves, so they’ll be coming here to make it difficult for us."
Kane believes the atmosphere at the derby was the best in the short history of the club's stadium and was pleased to reward the fans with a win.
He said: "The atmosphere was electric.
"The pressure was on us to deliver and we handled that really well. In a big game like this, at home, in our stadium, we had to win, otherwise Champions League was dead for us.
"So it was nice to respond that way, to show we’re capable of playing that way under that pressure."