Spurs moved level on points with second-placed United courtesy of a convincing 4-1 victory over Liverpool at Wembley on Sunday, taking full advantage of the Red Devils' shock 2-1 loss to Huddersfield Town a day earlier.
Mauricio Pochettino's side once again look like mounting a title challenge this season despite being five points behind current leaders Manchester City, but Kane admitted that the club need to start picking up silverware if they are to truly silence their critics.
"People will always have this little doubt about us until we start winning things," the England international told reporters.
"Performances and results like we produced against Liverpool was something we maybe didn't do as well at last year, so if we can continue that this year it will be good.
"With United losing at Huddersfield on Saturday, it gave us a chance to catch them up and next week is going to be a massive game. We're looking forward to it."
Kane, who helped himself to a brace in the win over Liverpool, has now scored 45 goals for club and country in 2017.