Spurs dropped to six points behind league leaders Liverpool with defeat at Turf Moor, prompting coach Mauricio Pochettino to concede defeat in his side's battle to stay in the race to win their top-flight crown in 58 years.
With 11 games left to the campaign, Spurs do not have much time to catapult themselves back into contention with the Reds and reigning champions Manchester City.
Many have already dismissed the London club's hopes of finishing top of the table this term, but England star Kane has backed his team to spring a surprise and claw their way back into the contest.
"It's been like that for the whole season. People have been talking about us not being in it, then we would win a few games and we'd be there," he said.
"People will probably say now it's a two-horse race, but that's not our problem. All we can do is take care of ourselves."
Kane made his return from injury to start against Burnley and find the net, only for Ashley Barnes to put the home side back on top late on.
The 25-year-old felt Spurs should have done enough to secure the three points and feels they must take it up a gear if they are to put more pressure on Liverpool and City.
"We're disappointed because it's a game we feel we should be winning, especially because we had a nice little break as well over the last 10 days or so, we were fresh.
"It's a shame because when we needed to find another level, another gear, we didn't have it in the locker. We've a tough week coming up, so we have to dust it off and be ready for that."
Kane's goal on Saturday takes him up to 15 goals in the league this season. He now sits two behind top scorers Mohamed Salah and Sergio Aguero.