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.
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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," said Kane. "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.
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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.
Kane looks to pile pressure on league leaders Chelsea
"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."
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