The striker scored Spurs' final goal at White Hart Lane as they beat Manchester United 2-1 on Sunday in the last match at their famous old home.
Tottenham's win ensures they have gone unbeaten at home for the first time in a league season since 1964-65 - and secured second place in the Premier League.
However, such positivity is tempered by speculation about the vultures circling overhead.
But Kane is determined they can turn what many perceive to be a negative into a positive.
It was the final match to be played at White Hart Lane before it is destroyed to make way for Spurs' new state-of-the-art structure. "We work so hard as a group and the staff, the manager, and, look, there's not many better teams to be at around the world at the moment", Kane said.
"We so badly wanted to win and now we get to enjoy it and say thanks to the fans for an awesome season, especially at the Lane. It's special to go a whole season unbeaten at home".
That bond has been clear throughout the season, with the Lane finale only underlining the link that extends to fans and club greats.
"It was unbelievable. It was the ideal send-off", he added.
"It's been a progression from (third) last season", Kane said.
On Monday morning Spurs chairman Daniel Levy handed over the keys to the stadium to Mark Reynolds, the CEO of a contracting company called Mace, who will oversee construction of the club's new stadium.
The stadium, home since 1899 and already being swallowed up by the new 61,00-seater ground rising around it, will be demolished with the club playing at Wembley next season before returning in the 2018-19 campaign.
Earth works begin at White Hart Lane just hours after Tottenham Hotspur's final game at the fabled football venue.
"We've got to believe".
And they certainly did.
However, Kane does not expect an exodus at a club he believes are still on the up.
"Only now say to our fans we will try next season to give our best and fight again to win the league".
Kane added: "I keep going back to the family".
"That's got to be our next step". We had to do it because, if I have Ashley Young, Luke Shaw, Marcos Rojo, Ibrahimovic, Tim Fosu-Mensah, if I have these guys, I can rotate, I can go for every match.
"It's an unbelievable stadium and we just have to make sure we feel comfortable there", midfielder Dele Alli said.