Spurs have gone 13 years without lifting a trophy, and Kane admitted he has a burning desire to win the "biggest prizes" in the game. The England international has been linked with a move away from north London, with Manchester United and Real Madrid as two names most heavily linked with a move.
Speaking after being named the Premier League player of the year at the London Football Awards, Kane said: "Individual awards are great, they are fantastic achievements. When I look back at the end of my career, I will go over it and take in a little bit more.
"The goal right now as a player is to win team trophies. As much as this [award] is great, I want to be winning the biggest prizes that there is to offer as a team and we are not quite doing that. It is one of those [situations], it is bittersweet. I would rather be winning team trophies and this award. It is what it is."
Kane added on Tottenham's current standing in England after their humbling against Man City: "We still have a way to go before we can reach that level of City and those teams at the top of the league. We've got to keep working hard, learn from it and try and finish the season strongly."
Tottenham sit seventh in the Premier League table with five games of the season remaining. They will need to leapfrog Liverpool and West Hame if they are to knock Chelsea out of the fourth spot and qualify for the Champions League.