Spurs fell 5-0 down at St James' Park within 21 minutes in a shocking defeat that culminated with interim boss Christian Stellini being sacked on Monday. The squad reimbursed fans who made the journey to watch the game.
Earlier this week, Levy revealed he met with senior players, and Kane said the meeting played a part in helping the team refocus for the run-in.
"The chairman asked for a meeting," he told Standard Sport on Thursday. "I think it was important [for him] to understand where the players' heads were at that moment, coming off the back of that result. And it wasn't just that result, it had been building up since we conceded the two goals 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. We're still fighting for fourth place, but if not fourth, we'll try to finish fifth or sixth, as high up as we can.
"In this league, it's so competitive, you can easily end up eighth or ninth if you're not careful. I'm glad we reacted like that last night.
"When you travel that far [Newcastle] and you're 5-0 down in 20 minutes, it's not acceptable on any level, so we know [refunding fans] wasn't going to magically change their feelings or make the result any better, but it was still something as a group we wanted to do to try to show we're all together in this moment."
Ryan Mason assumed Stellini's position and led Spurs to a spirited 2-2 draw against Manchester United on Thursday, with his side scoring two second-half goals to fight back after falling to an early 2-0 deficit.
Kane praised Mason, who had just three days to prepare for the clash against United, saying the squad are "fully behind" the interim manager after their strong second-half showing on Thursday.
"Ryan has been great," he said. "He's come in at a really difficult time after that [Newcastle] defeat and he's not had long to implement any style, so it's all been about motivation and getting some belief back in the boys.
"I've known Ryan a long, long time. He has a great football brain. He sees the game in a really good way, he has worked under some fantastic managers.
"We're all behind him. We want to work for him and try to finish the season as strong as we can. And he's a great guy and a great manager. Hopefully, we can finish strong and see what happens."
Spurs look to reignite their hopes of a top-four finish as they visit Liverpool on Sunday.