John Stones and Ross Barkley made costly errors as two extra-time goals earned Ronald Koeman's men a place in Sunday's final against Portugal.
England had led through Marcus Rashford's first-half penalty only for Matthijs de Ligt to head home an equaliser.
The Three Lions thought they had scored a late winner through Jesse Lingard only for VAR to rule the strike out for offside and England unravelled in the additional time, with Kyle Walker's own goal and a Quincy Promes effort doing the damage.
"We came out a bit slow in the second half but we managed to step it up again, moved it better and scored a goal we thought was the winner," Kane told Sky Sports.
"But there are fine margins in big games like this and it didn't go our way. Mistakes were made but we learn as a team, take it on the chin and that's the way we want to play.
England also fell at the semi-final stage at the World Cup last year, losing to Croatia in extra time, and Kane accepted England did not cope well enough with Netherlands' pressure.
"We made some sloppy mistakes in giving the ball away too easily, they got pressure on us quite high but we have to deal with that," Kane added.
"When you come up against good teams, like Croatia at the World Cup, this is what they do and you have to get used to that.
"Holland are a fantastic team, as were Croatia, and fine margins have decided it again, whether it's offside or goals from set-pieces.
"It is what it is, we're disappointed but we have to learn from it."
Despite the setback, England are off to a flying start in Euro 2020 qualifying, having won their first two matches and rolling to a plus-nine goal difference.