The Spurs striker is expected to be at the centre of transfer speculation after his club lost the League Cup final to Manchester City last weekend and Kane wants to earn more than individual honours.
Speaking after being named Premier League Player of the Year at the London Football Awards, Kane said: "When I look back at the end of my career, these are all the things I'll go over and take in a little bit more, but the goal right now as a player is to win team trophies.
"As much as this is great, I want to be winning the biggest team prizes. We're not quite doing that. It's bittersweet, but it is what it is. I'm proud to win [Premier League Player of the Year], it's been a good season on the pitch."
Kane did speak of his pride at claiming the award given the number of quality players at London clubs in the Premier League.
He said: "I'm from London, so growing up and having that local feeling, there is nothing better than playing for your local team, the ones you have been brought up around.
"London will always have a special place in my heart. It's where I'm from and where a lot of my family are from. It's a special award to win for sure.
"There are so many great players based in London. To win this award is a great achievement."