The Three Lions, who lost to Iceland in last-16 round of the Euros, have started a new era under manager Sam Allardyce with a 1-0 win over Slovakia in their opening World Cup qualifier on Sunday.
"We wanted to get off to a winning start, and we fully deserved the win," Kane said.
"It looked like it was going to be one of them games where the ball wouldn't fall in the back of the net but we kept at it, we were patient and I was delighted for Adam to get the goal.
"Getting back to winning ways and putting things right is the way to put the Euros behind us. We were delighted about that."