Mauricio Pochettino's side twice came from behind to draw level with Chelsea before goals from Eden Hazard and Nemanja Matic condemned Spurs to a seventh successive FA Cup semi-final defeat.
Kane admitted he is envious of Tottenham's London rivals' ruthlessness after Chelsea booked their spot in the final despite being dominated for large spells.
"They beat us twice and we beat them once so that’s what’s disappointing," Kane said. "We want to find a way to win these sorts of games. We dominated large spells but Chelsea found a way to win.
"It was similar a couple of years ago, in the (2015 League) cup final, we dominated that as well. It is disappointing and hard to take. I can’t really put a finger on why, it was kind of a bit of luck and then momentum swung their way. It was hard to come back from.
"They have a great team and a great squad. Whoever comes into their squad is a great player and we were just focused on us. We set out in an attacking way and we wanted to be on the front foot.
"Even though we went behind quite early, I thought we dominated the game and had the better chances. That’s why we are so disappointed that we didn’t go on to win the game."
Tottenham face Crystal Palace away on Wednesday as they look to close a four-point game at the top of the Premier League. Chelsea, who are league leaders, will face Southampton on Tuesday at Stamford Bridge.