Spurs have surrendered the top four spot to Arsenal after losing to Brighton and Hove Albion and drawing against Brentford in their last two matches.
Antonio Conte's side now find themselves in fifth place, two points behind the Gunners.
Tottenham have some tricky ties in their remaining fixtures as they face Leicester, Arsenal, Liverpool, Burnley and Norwich City.
"To only get one point from those two games [Brighton and Brentford] is disappointing," Kane told Standard Sport.
"We're running out of games in terms of dropping points.
"There are five games left and we feel like we are pretty much going to have to win all of them to get that spot. We are more than capable of doing that, we believe in that and that is what we'll try and do.
"Is it still in our hands? Yeah. If we win the last five games we will be in the Champions League, so that is how we've got to look at it."
"We know those five games will be difficult, we go to Liverpool away as well which will be very tough," he added.
"As we've seen this season, we have dropped points against teams where we were probably expected to win and so have the others around us. It is by all means not done yet.
"We have to stay focused and keep working hard. We have a little gap now to prepare and work and hopefully, we can put in a good performance against Leicester [on Sunday].
"It has been a long season and we've definitely had ups and downs this season. I think we've done great to put ourselves in this position we're in now but it is about who can finish it off.
"That is the most important thing in football. Hopefully, it is us, we will work as hard as we can to make sure it is us and get that Champions League spot."
