Kane scored a 28th Premier League goal of the season - a stunning 25-yard free-kick - as Spurs slumped to a 3-1 defeat to Brentford in their final home game of a miserable campaign.
The England captain is entering the final year of his contract and has attracted interest from Manchester United and Bayern Munich.
Asked by Standard Sport if Saturday’s loss could have been his final home game for the club, Kane said: "I’ve said all along I’m focused on this season and trying to help the team as much as possible. That’s all I can do.
"There’s a big summer ahead and a lot that needs to change here to start being successful again. Ultimately my focus now is to enjoy this last week as much as possible and try to finish with a win [at Leeds United] on Sunday."
Levy has already appointed a new chief football officer, set to start work in July, and is due to name a new head coach and sporting director at the end of the season.
Kane added: "I think there’s a conversation [with the chairman] to be had anyway in terms of some of the values of the club. It will be a conversation, we’ve had many conversations before like that on how we can improve, and that will be the case again."
Before Saturday’s game, the club unveiled a mural of Kane outside the stadium to commemorate him becoming their all-time leading goalscorer, while his magnificent strike to break the deadlock means he is the first player to score in 25 different Premier League games.
Afterwards, he scooped a hat-trick of the club’s player-of-the-season awards but the squad’s lap of honour was soured by Brentford’s second-half comeback.
"I’m extremely grateful to the guys for doing [the mural]," Kane said. "It’s nice to have those memories. I was there with my family and kids and it was nice for them to see that as well. As always these things never feel quite as good when you don’t get the result the next day. Even walking round the pitch doesn’t feel as good. That’s life, we have to take it on the chin and get ready for next week.
"It’s hard. You feel responsible. We wanted to send the fans home happy. You want to enjoy the moment with your family but the fans can’t enjoy it as much as we would have done. We have to keep battling, keep working and try to send the away fans home happy on Sunday."
Acting head coach Ryan Mason experimented with another new system, with Kane supported by three interchanging forwards in a bold 4-3-2-1 formation.
Kane admitted the squad wants the season to end but says they had hoped to finish on a high note.
"It’s been a difficult season," he said. "I think we want it to end but we wanted it to end on a couple of wins. We fully believed that was possible after the way we played in the first half.
"Brentford are only a point behind us so it shows any team can punish you. The league is getting tougher and if you don’t keep on top of things you can find yourself dropping down to mid-table and that’s where we’ve been in the last couple of months.
Kane added: "Ryan is trying to help us as much as possible. We changed the system again and I thought it worked great in the first half.
"Sometimes these things take time. The type of training, energy and fitness takes a while to build up but when you’re in middle of the season with few games to go you haven’t got the chance to do that.
"You have to somehow be able to win games even when you’re not at your best. We’re struggling to hang into games when there’s a little bit of pressure against us. That was what happened there and we weren’t able to recover from it.
"First half we probably should have been 2-0 or 3-0 up, we weren’t clinical enough in those moments. In the Premier League you can be punished. We’re disappointed with the way we came out in the second half. We didn’t play with the same intensity or energy and we got punished for it. That’s been the story of our season, there have been some good halves and some bad halves as well and that was on show.
"It’s been a tough season for a lot of the players. It’s never easy playing at this highest level and performing week in and week out. That’s what separates the best teams from the teams where we are now. I’ve said all season long we have to show more consistency but it’s easier said than done. There’s still a lot of work to do and all we can do now is prepared for the final game of the season."