With second-placed Liverpool away to Manchester United on Sunday and Manchester City not in Premier League action this weekend, Spurs went into their match knowing there was a realistic chance they could have closed to within just two points of the top two.
But at Turf Moor Spurs came unstuck, as Ashley Barnes netted a late winner after Kane had cancelled out Chris Wood's opener.
A win for Liverpool at Old Trafford will leave Spurs eight points off the top and arguably end their title hopes after a recent resurgence, a situation not lost on Kane.
"It's very disappointing," Kane told Spurs' official website. "It was one of those games, a tough battle, a dry pitch, we know how Burnley play, especially at home and it was physical.
"We did well to get back into it at 1-1, but we couldn't find the next level to push on and get the win and then unfortunately we conceded again.
"It's a game we should be winning. We had time off, so we were fresh and we expected to come here and step it up a level and give it a massive push for the rest of the season.
FULL-TIME: Burnley take the points on a disappointing afternoon at Turf Moor. pic.twitter.com/52u56tEt3c— Tottenham Hotspur (@SpursOfficial) February 23, 2019
"Now it puts us behind and in a tough position. It's a big week to come and we have to move on as best we can.
"It's a big period for us and we know we are more than capable of winning these games. Burnley was disappointing, but we have to move on and it's a big game against Chelsea next."
Tottenham take on Chelsea at Stamford Bridge on Tuesday before hosting Arsenal the following weekend.