Gareth Southgate's team opened the scoring at the Luzhniki Stadium, but Croatia turned things around and will now face France in Sunday's showpiece finale.
The defeat will be hard to digest for England, who have won many admirers for their run to the semifinals and must have felt they were on the verge of the final when they were in front.
"We gave it everything, I know we're gonna look back and say we could have done this and what but at the end of the day it was small margins in a big game and it didn't go our way today", said striker Kane, now the tournament's top scorer with six goals.
In the 90th minute, England was granted a free kick just yards from Croatia's penalty box, but Trippier's shot to Kane's head failed to make it to the back of the net.
For Croatia, it's on the brink of arguably the most shocking World Cup title run in modern history.
England, playing with zip and objective, looked sharp going forward as a rattled Croatia side tried to regroup, with Raheem Sterling proving a real handful but the score remained 1-0 at the break.
But Croatia came out for the second-half on top of the Three Lions, and equalised with a goal from the outstanding Ivan Perisic.
"But it's small margins, in extra time we get a corner cleared off the line".
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But Andy Bradley, 42, from Hull, felt the team had done the nation proud. John Ryan, 33, from Coventry, was in the Luzhniki to witness the defeat.
As the extra period started Croatia struggled to maintain their intense pressure but continued to threaten the England defense.
Croatia equalised in the 68th minute, thanks to a goal by Ivan Perisic who profited on some weak defensive work by England, who looked below-par in the second half.
Match stats from the Croatia v England Fifa World Cup semifinal in Moscow.
"It's tough. We are gutted", said Kane.
"It hurts, it'll hurt for a while, but we can hold our heads up high". It's been a fantastic journey. I'm hugely proud of what we've done - I couldn't have asked for any more.
"We had a good spell we went one nil up and we had a couple of chances we're we could have got another". But we've fallen just a bit short.
Telesport's Juraj Vrdoljak compared Croatia's second-half comeback to an "adrenaline-driven man lifting a truck to save his child".