Spurs demolished United 3-0, with a goal from Kane himself and two from Brazilian winger Lucas Moura. This win was Tottenham's third of the season and takes them up to second in the table, behind Liverpool on goal difference.
Quoted by the Daily Star after the match, the England captain claimed that the victory at Old Trafford serves as a warning to the other title contenders as to Tottenham's capabilities.
''It's massive, just what we needed,'' Kane said, ''We wanted to put a statement out there.
''We need to kill off teams, especially away from home. After that goal we had the high press, we were playing it quicker, moving in behind and punishing them when we needed to.
''We took our chances and coming here to Old Trafford and winning 3-0 is a big, big result.''
Tottenham have gone under the radar in regards to who will compete for the title, with much of the talk being about Liverpool and Manchester City. However, following their impressive start, Tottenham can definitely consider themselves potential title winners come May.
Kane said: ''We wanted to start the season well and three wins out of three is a great start.''
Spurs fans can be extra pleased with their start to the Premier League, as in previous seasons the club have had a slow start to the season, something Kane acknowledges, adding: ''We haven't started well in previous years, we've had to play catch-up, but the top six are so strong now you have to stay with them.
"This will give us huge belief, it's a great statement tonight. We're trying to create our own history at Spurs."
Many critics of Tottenham have highlighted their lack of new signings as a reason for potential struggles, however Kane disagrees, arguing that in some ways it has been an advantage: ''A lot of us have been playing together for a while and that helps.
''The gaffer said he's not bringing in players who won't improve the squad and that's a big bonus for us.''
Tottenham's next match is an away visit to Watford who have also won all of their games so far. This means that come Sunday, at least one of the top four teams will no longer hold on to a perfect Premier League record.