"We're buzzing. It's probably not sunk in," Kane said.
"We know there is still a big game ahead but we are feeling good, confident.
"We were composed, we controlled the game. We've just got to keep doing what we are doing.
"We're enjoying it, the fans are enjoying it, I'm sure we'll see some videos later of the fans enjoying it."
Maguire's thumping header gave the Leicester centre-back his first international goal, just two years after watching Euro 2016 in France with his friends in the stands.
"It (the first goal) can't come better than that. The win sends us through and that's the main thing," Maguire said.
"We felt like we could dominate the ball in this game. It was a little bit sloppy at the end of the second half, we felt it was a bit too open."
Tottenham midfielder Alli nodded in only England's third goal from open play of this World Cup so far just before the hour mark, having struggled with injury earlier in the tournament.
"It's a great achievement for the team... Owed it to the fans back home who believed in us," he told the BBC.
"Always nice to score, especially on occasions like this. I don't think this was my best performance on the pitch. But it's an amazing feeling to be going to a semi-final at a World Cup.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)