This comes amid continued speculation over his future.
England captain Kane, 27, is yet to win a trophy at Spurs, with the loss to Manchester City his third in a final.
The Spurs academy graduate described the season as “disappointing”, with the club seventh in the Premier League.
“I want to be winning the biggest prizes there are to offer and we are not quite doing that,” Harry Kane said.
Harry Kane has his current contract run until 2024 but he has been frequently linked with a move away in recent weeks.
He has scored 31 goals in 44 appearances this season and this week won the Premier League Player of the Year at the London Football Awards.
“Individual awards are great – they are fantastic achievements,” Kane told Sky Sports.
“When I look back at the end of my career, these are the things I will go over.”
“And take in more but the goal right now as a player is to win team trophies.”
“It is bittersweet. I would rather be winning team trophies and this one but it is what it is.”
“I am proud to win it; it means it’s been a good season on the pitch.”
“So I have got to try and continue what I am doing.”
Harry Kane was named Premier League Player of the Year at the 2021 London Football Awards on Tuesday.