Mauricio Pochettino’s side headed to Old Trafford on Monday looking to put down a marker and keep pace with the early leaders in the English top-flight table.
They were able to make the most of the struggles currently being endured by the Red Devils, with a convincing win prolonging a faultless start to the season.
With maximum points taken from three games so far, Kane believes Spurs have shown that they need to be taken seriously in the 2018-19 battle for domestic supremacy.
The England international, who opened the scoring against United before Lucas Moura bagged a brace, told Tottenham’s official website: “It’s massive, just what we needed. We wanted to put a statement out there.
“We knew it was going to be tough and it was, especially in the first half, it was a battle out there.
“We said at half-time we needed to step it up a gear and that’s what we did. In these games, the first goal is so important - getting that breakthrough - we got it and punished them after that with two great goals from Lucas.
“We need to kill teams off, especially away from home. After the goal we had the high press, we were playing it quicker, moving in behind and punished them when we needed to. We took our chances and coming here to Old Trafford and winning 3-0 is a big, big result.
“It’s great for us, great for the fans, great for the club. The fans will travel home happy and that’s what it’s all about. As a club, we want to stay at the top of the league and the only way to do that is by coming to places like this and getting results, so today is a huge statement.”
Tottenham’s next outing will see them face a fellow in-form side, with a trip to Vicarage Road set to see two perfect records put on the line in a meeting with Watford.