The result means Spurs are now seven points off the Champions League positions and with an inferior goal difference to the other teams in the mix.
And while the England international concedes the odds are against Tottenham, Kane reckons the team can finish in the leading pack if they go on a winning run.
“It’s going to be tricky, we’re quite a few points behind now,??? the 21-year-old said.
“In this league you never know. We’ve got winnable games coming up and we focus on them. We take each game as it comes and see where that takes us.”
Kane was captain for the day at Turf Moor, but he endured a frustrating afternoon as his 30th goal of the season proved elusive against Burnley.
“I was disappointed to not to get on to the scoresheet but that’s football and I just have to dust myself down and work on it and make sure that I get onto the scoresheet for the next game,??? Kane said.
“It was a real honour, a very proud moment for myself to lead the side out. It’s very special for me. Hopefully there is more to come in the years to come.
“We’ve got a lot of leaders in the team. It’s a very young team and everyone has their say. To be given the armband by the gaffer is a proud moment. But there are a lot of captains out there and we all try and work to the same aim.”
And Kane, who said the experience of playing against Italy in midweek was “tough”, admits there is suddenly a lot of competition among English strikers, including Burnley???s Danny Ings.
“It was a great experience in Italy. To get my first start for England is another proud moment for me. It was tough and I can only learn from those sort of games,??? Kane said.
“I know Danny well from the Under-21s. He scores goals and his movement’s great. He’s a prospect for English football.
“There are a lot of great English strikers here at the moment, which is good for the country. There’s competition. We’ve all got to work hard to retain our place.”
Meanwhile, Kane thanked Queens Park Rangers striker Charlie Austin, after one of his biggest rivals for the Premier League’s Golden Boot revealed the Spurs forward was his choice to be the player of the year.
“I don’t think we cannot give it to him. He’s been the outstanding player,” Austin said last week of Kane.
And Kane said: ‘It’s great to hear. He’s done fantastic himself and to have him vote for me is great. I spoke to him when we played them away from home – he’s a good lad and we get on well.”