Kane was desperate to leave Tottenham to join Manchester City this summer and tried to engineer a move away, reporting late for pre-season.
But Tottenham flat out refused to negotiate with Manchester City and the 28-year-old finally relented on Wednesday and confirmed that he will be staying at the club this summer.
Kane remains popular amongst a large section of the Spurs fans, but there were chants against him in the opening game of their season against Manchester City.
Carragher believes the striker understood that there was no way for him to leave Spurs without irreparably damaging his relationship with the club and their supporters.
He feels that is unlikely to change next summer if Kane wants to leave again and believes the striker must considering staying at the club for the rest of his career to protect his legacy amongst the Tottenham fans.
Carragher wrote in his column for the Daily Telegraph: “The fans’ response felt like a critical moment.
“Kane would have imagined leaving north London with a handshake and understanding given his service to the club, Spurs consoled by how much they received for him.
“Sensing the mood turn against him will have deeply hurt and worried him.
“He knew there was no way of leaving on good terms, and no way of guaranteeing an invitation to any post-career reunions.
“That is not going to have changed by next January, or next summer, so I would strongly recommend against Kane going down the route of prolonging this saga into future transfer windows.
“Having accepted staying at Spurs for now, Kane would be wise to make peace with the idea of doing so for good, and embracing one of football’s eternal truths: ‘Your name is more important than any trophy’.”
Kane has made it clear that he wants to win the biggest trophies on offer, which seems unlikely at Tottenham for the moment.
