A year at Wembley awaits to allow completion of their new 61,000-seater stadium on a site adjacent.
Mauricio Pochettino felt privileged to witness the final game at White Hart Lane as Tottenham gave their home the flawless send-off with a 2-1 win over Manchester United.
"What a way to finish", Kane said after fans flooded the field at the final whistle.
He added: "We've just got to next season go out and try and win some trophies, and go into the new season as proper title contenders and players who can win trophies".
Spurs play their final game of the season away at Hull at the weekend and will play their home games at Wembley for the 2017/18 season. "We've got the team, we've got the belief, so next season hopefully it's our year".
The result means that Spurs have confirmed a second-place Premier League finish and are unbeaten at home this season.
That used to be United's status, but it hasn't come close to a record-extending 21st English title since Alex Ferguson retired in 2013.More news: House Oversight Chair Jason Chaffetz Announces Resignation From Congress
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The first half saw Tottenham boss the game and took the 1-0 lead early in the 6th minute from a Victor Wanyama header.
Four points off the top four, Mourinho has abandoned hope of qualifying for the Champions League via the league and is likely to rest players after Thursday's Europa League semi-final success against Celta Vigo.
He also explained that the team are "sad and disappointed that Chelsea won the league" but he also believes "there is nothing to regret" and that "we will be proud of our achievements and we fought for the Premier League".
"When people say "we gambled", we didn't gamble, we didn't choose Europa League. We had to do it". In that time, Tottenham has spent about as much as it has recouped on transfers. That's progression from last season and we have to keep it going now.
By avoiding defeat on Sunday, Pochettino and his disciples have gone the entire 2016/17 unbeaten in the league.
"This has been a proper send-off to what has been an awesome stadium for us".
Club greats were welcomed onto the pitch one by one after Tottenham had beaten Manchester United 2-1 in their last game at the Lane, Spurs' home of 118 years, which is being demolished and rebuilt.