The Spurs striker provided the final touch on John Terry's opener at Wembley, helpless as the ball deflected off him into his own net - but spared the dishonour of an own goal, given the on-target shot from the Chelsea defender.
Kyle Walker was not spared the same fate, however, as Diego Costa's strike from an acute angle struck Tottenham's full-back and beat goalkeeper Hugo Lloris.
Kane said Chelsea were lucky in both of their goals but it did not make defeat in the showpiece any easier to take - as Tottenham's title drought, which has seen them trophy-less since 2007-08, was extended.
"It's the worst feeling in the world losing, and losing in a final on the big stage even worse," Kane told Spurs TV.
"When you see Chelsea lift that trophy at the end it gives you that fire in your belly.
"It's disappointing - the lads gave it everything and I thought we played well.
"In these big games you don't always get the luck you need and I felt Chelsea did with a couple of deflected goals which on another day wouldn't go in."
Kane said the message from manager Mauricio Pochettino was that their run to the cup final was not without merit, especially given the Argentine only took over at White Hart Lane this season.
"Just to be proud of ourselves. We've come a long way. It's a very young team with a new manager," Kane added.
"To be in a final in the first season is great."
Kane is without a goal in his past two games in all competitions, but has six goals in his past four Premier League appearances ahead of Spurs' hosting of Swansea City on Wednesday.
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