The Three Lions thumped Ukraine 4-0 in Rome on Saturday to set up a last-four showdown with Denmark at Wembley.
Kane scored twice with Harry Maguire and Jordan Henderson also netting at the Stadio Olimpico.
They welcome Denmark on Wednesday with Kane admitting the pain of their World Cup semi-final defeat to Croatia three years ago remains an inspiration.
“Obviously there are a few of us in this team who played in that semi-final and we know how much it hurt not getting to the final and go all the way,” he said.
“It has been a great tournament so far and we have ticked off the boxes as we have gone along but the bottom line is we have a vision of where we want to be and it has to be winning major tournaments.
“We are on the right track but we have a very tough game coming up. We have our supporters there as well, we are going to have 60,000 in the stadium and we want to do them proud and friends and family proud.”
The Tottenham striker also insisted his slow start to the tournament never played on his mind. Kane has three goals in his last two games after failing to score in the group stage.
“I have said all along as a striker the ball falls your way and sometimes it doesn’t, today obviously it fell my way early,” he said.
“To get one early in the second half was important, I nearly got the hat-trick but Hendo scored from the corner anyway. That is part of being a striker. You have to be ready for the next opportunity and I will be ready for Wednesday.”
England have kept seven straight clean sheets and are yet to concede at the tournament.
Kane added to the BBC: “That’s what we’re building on. We don’t get carried away. We have a great unit from front to back and it’s a vital part of winning games and tournaments.
“We have more experience, we have been playing for our clubs in big games, a lot of us in the biggest of games – Champions League finals and Premier League title races. We are looking confident out there.”
Kane also praised England boss Gareth Southgate for his leadership and focus.
He said: “Gareth has been brilliant. I’ve known him for a long time. I’ve had him with under-21s through to the senior squad now and he just brings a real calmness to the squad, a real togetherness.
“The most important thing for him is for us to be together. Whether you’re playing, you’re on the bench or you’re in the squad, there is a real team environment and all pushing in the same direction.
“He’s a fantastic coach, he has great ideas. He does it how he wants to do it.”