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The Three Lions reacted the final of Euro 2020 on Wednesday evening after running out 2-1 winners at Wembley.
Kane scored a rebound winner after his penalty was saved by Kasper Schmeichel - a penalty won by Raheem Sterling.
He darted into the box before being hauled down by Joakim Mæhle, with many believing it was soft.
Carragher has defended the Manchester City winger in his latest Telegraph column and the manner in which he won the penalty.
He begun: "I have no problem with how Sterling 'won' the spot-kick. He did what many top-class attackers have done when Mæhle brushed against his leg. He was savvy, not cynical.
"To me, it was not cheating because having dribbled into the penalty area he induced panic in those trying to stop him. They got the man rather than the ball, regardless of how bad it really was.
"This is what makes Sterling such a dangerous player, running at pace so defenders never know whether to risk a challenge, especially in the penalty area.
"In a situation such as Wednesday night's, the defender's biggest mistake is in being too late to his man, making contact inevitable and ensuring the officials have a big decision to make, with a volatile home crowd screaming for what in that split second looks like the most obvious foul.
"I would not have been happy with the referee for penalising me in those circumstances, but I would have been more livid with myself and my full-back for allowing Sterling to get so far towards the six-yard box."
Kane, meanwhile, wanted a penalty after colliding with Christian Norgaard with VAR even checking the incident.
Carragher pointed out that Kane's style of play has changed since last-16 victory over Germany last week.
The former Liverpool defender continued: "England were never going to be able to get this far unless we saw Tottenham's Kane. We have done so when it has really mattered in the quarter-final and semi-final; drawing fouls, dropping deep and making clever passes.
"He is the best passer in the squad. Look at the delivery to Saka in the build-up to the equaliser against the Danes.
"It was never about doubting Kane as a player, or whether he should stay in the side in the knockout stage, or if the goals would come.
"It was about cold, hard analysis of each 90 minutes and seeing and saying it as it is, asking what he brought to the team outside the box as much as in it. There had to be huge improvement. There has been."
England will now face Italy in the final on Sunday evening.
Featured Image Credit: Sky Sports & ITV Football
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