The debacle at Newcastle, which more or less put an end to Tottenham's top-four hopes, resulted in the players reimbursing fans' costs for the trip to Tyneside.
It also cost stand-in manager Cristian Stellini his job, with former midfielder Ryan Mason taking charge of Thursday's battling 2-2 home draw against Manchester United.
After the United game, Kane said talks were held with the under-fire Levy, who many Tottenham fans blame for the club not winning any silverware since 2008.
"The chairman asked for a meeting," Kane, the club's record scorer said. "Obviously I won't go into what was said but I think it was important (for him) to understand where the players' heads were at in that moment.
"Obviously coming off the back of that (Newcastle) result and it wasn't just that result, it had been building up since the international break when we conceded twice against Southampton.
"It was an honest conversation of where everyone is at and what we need to try to do to give us the best possible chance to finish the season with something."
Tottenham responded well to going 2-0 down at home to United with goals by Pedro Porro and Son Heung-min lifting the mood of gloom hanging over the north London club.
Mason, who had a previous spell in charge following the sacking of Jose Mourinho, said the comeback had created good energy ahead of Sunday's trip to seventh-placed Liverpool, a fixture vital to the club's hopes of at least qualifying for next season's Europa League.
"In football, negativity can spread very quickly but at the same time so can positivity, if you create the right feeling," the 31-year-old Mason, forced to end his career after a head injury, told reporters on Friday.
"That can accelerate a process so hopefully we can continue with what we saw in the second half (against Man Utd). We were together and had belief in what we were doing."
Mason said anger had fuelled Tottenham's improved performance against United.
"Naturally when you have a result like last Sunday there should be anger, I wanted to see an angry team," he said.
Tottenham's draw put them back in fifth place but they are only a point ahead of Liverpool, who have a game in hand, and are level on points with sixth-placed Aston Villa.
The clubs finishing fifth and sixth are almost certain to qualify for the Europa League.
"The game on Sunday will not determine the outcome of the season, (but) Tottenham and Liverpool in any season is a big game," Mason said.
Tottenham will again be without keeper Hugo Lloris who went off injured at half time in the defeat at Newcastle with his side already losing 5-0.
