Mauricio Pochettino's side came up short in the title race for the second successive year after Chelsea repelled their determined challenge in the same way Leicester City frustrated them 12 months ago.
Deposed champions Leicester are Tottenham's next opponents at the King Power Stadium on Thursday, but Kane's thoughts are already turning to next term.
Watching Chelsea's jubilant players celebrate their title triumph was a painful experience for Tottenham striker Kane, who once again has more than 20 goals to his credit without winning a major trophy.
Even so, Kane is convinced it will be Tottenham's turn to hoist the silverware sooner rather than later because Pochettino has built a gifted group that revels in the team-first ethos preached by their manager.
"Everyone just has a special connection here. It's a special bond and I don't think you always get that at clubs," Kane said.
"That has to motivate us to hopefully be out there next year lifting a Premier League together.
"That's got to be the next step. That's got to be our aim and we've got to use this as motivation to get there."
Tottenham said an emotional farewell to White Hart Lane on Sunday, with a 2-1 win against Manchester United the perfect send-off for the 118-year stadium before it is demolished it make room for a new arena.
Tottenham's runners-up berth is their best league finish since 1963, but the progress of Pochettino's side has inevitably prompted reports that several key players could be lured away by bigger clubs in the close-season.
Kane is unmoved by such talk and says Spurs' trajectory makes them as attractive as virtually any club in the world.
"We're a family on and off the pitch. We work so hard as a group. Look, there's not many better teams to be at around the world at the moment," he said.
"We've got a very bright future, a great squad, a team that's hungry to win and to learn and to get better.
"Of course there's going to be rumours over the summer, but I think I'd be very surprised if most of us ain't still here next season."
Despite all their promise, Tottenham are yet to win a trophy under Pochettino and their last major prize was the League Cup in 2008.
They face the added problem of playing their home games at Wembley next season while the new stadium is built.
Yet, ignoring his team's poor results at the national stadium in recent years, England star Kane is adamant they should be aiming high next term.
"Imagine what it would be like winning a Premier League, or winning an FA Cup or a Champions League or something?" he said.
"That's got to be our next step. We're young but we're getting more experience year in, year out.
"We've just got to go and make it happen. We've got the team, we've got the belief, so next season hopefully it's our year."
After their fairytale title last season, this has been a turbulent campaign for Leicester, with poor league form leading to Claudio Ranieri's sacking before a memorable run to the Champions League quarter-finals under Craig Shakespeare.
With two home games left, it could be a long goodbye for Algeria winger Riyad Mahrez, who remains a target for several clubs despite an erratic campaign from last season's PFA Player of the Year.
"You don't have a decision to make unless you get an offer, and we haven't had an offer for any one of our players," Shakespeare said of the transfer talk.
"There is always going to be speculation because they are good players."