Spurs secured a second-place finish in the Premier League by defeating Manchester United 2-1 on Sunday, Kane following up Victor Wanyama's header to secure victory in the club's last game at White Hart Lane, four years after selling Bale to Real Madrid for €100million.
"We're a family on and off the pitch", Kane told British media.
"We've got to get the fans behind us, we've got to keep the fans believing and, look, we have got to just believe in ourselves". 'It's a good place to be and with the manager we've got here, I can't see many better places for me personally to improve.
"We've got a very bright future, a great squad, a team that's hungry to win and to learn and to get better".
The next step for both Pochettino and Tottenham will, inevitably, be to win a trophy.
They have tied down a host of key men in the last 12 months including skipper Hugo Lloris, Harry Kane, Christian Eriksen, Jan Vertonghen, Eric Dier, Kyle Walker and Danny Rose.
"Imagine what it would be like winning a Premier League, or winning an FA Cup or a Champions League or something?" he said. "I'm happy to be part of the team when we're playing like this", he added. I know they have got a long waiting list for season ticket holders but it can go backwards quickly.
"It's important we don't forget about what happened and how far we've come".
Two matches of the season remain for the north London club, with a trip to Leicester City on Thursday and already-relegated Hull on the last day of the season awaiting them.
Alli has been a revelation at White Hart Lane over the past two seasons and he has won back-to-back PFA Young Player of the Year awards for his performances.
Many of their key players have been attracting admiring glances, yet Kane is unmoved by such talk given Spurs' trajectory makes them as attractive as nearly anyone.
"It's frustrating when we've played as well as we have, it's very frustrating when you don't have anything to show for it".