Matthijs de Ligt cancelled out a Marcus Rashford penalty to force extra time in the last-four clash, and it was Netherlands that triumphed courtesy of an own goal from Kyle Walker and late Quincy Promes strike.
Ronald Koeman's side will now face Portugal in the final of the competition on Sunday night, leaving England to take on Switzerland in the third-place playoff earlier in the day.
Netherlands had a sight of the England goal in the seventh minute when a poor pass from Ross Barkley led to Memphis Depay working some space outside the box. However, the former Manchester United attacker saw his strike closed down by John Stones, who lined up alongside Maguire at the heart of the defence.
Pickford had to make another stop to keep out a strike from Depay in the 20th minute as Oranje continued to look the team more likely to make the breakthrough in the second Nations League semi-final.
Frenkie de Jong was running the show in the middle of the park with the likes of Declan Rice, Fabian Delph and Barkley struggling to get near the midfielder, who will turn out for Barcelona next season.
England were awarded a penalty in the 30th minute, however, when a loose touch from De Ligt led to the Ajax captain hacking Rashford to the ground. The Manchester United forward stepped up and sent his spot kick into the bottom corner to hand Gareth Southgate's side the lead.
Ryan Babel tested Pickford's reactions from distance in the period that followed before England had an excellent chance to score a second. Excellent work from Jadon Sancho released Rashford inside the Netherlands box, but Denzel Dumfries was across to make a brilliant challenge.
Cillessen then had to keep out a strike from Delph after Maguire, who could leave Leicester City this summer to join United or Manchester City, had kept the ball alive inside the Netherlands box.
De Ligt had the opportunity to make up for his error in the latter stages of the first period when he met a cross from Depay, but the centre-back's header dropped wide of the Three Lions post.
England were forced into a half-time change, with Harry Kane taking the place of Rashford, who took a few heavy challenges in the first 45 minutes of action.
The Netherlands had a huge shout for a penalty early in the second period when Ben Chilwell appeared to hack Bergwijn to the deck, but neither the referee nor the linesman was interested.
England then had a glorious chance to double their lead in the 55th minute when Sancho met a cross from Delph, but the Borussia Dortmund attacker headed straight at Cillessen before Depay tested Pickford down the other end after a poor mistake from Walker in a defensive position.
Netherlands were having an awful lot of the ball as the match headed for the 70th minute, but Koeman's side were finding it difficult to create clear-cut chances, with Pickford comfortable with the strikes from distance.
Promes and Donny van de Beek both came off the Netherlands bench in the 68th minute, moments before Stones headed a Chilwell free kick just wide of Cillessen's post as England threatened a second.
Promes had a powerful strike deflected behind for a corner in the 72nd minute as Netherlands continued to force the issue, with England struggling to get out of their own half.
Eventually the equaliser came in the 73rd minute when De Ligt climbed above Stones and Walker inside the England box to thump a header into the back of the net and it was no more than Koeman's side deserved for their intense pressure.
Van de Beek should have scored a second for Netherlands in the 78th minute when the ball dropped for the Ajax midfielder inside the Three Lions box, but he fired over Pickford's crossbar.
England thought that they had regained the lead in the 83rd minute when Lingard finished an excellent team move involving Chilwell, Sterling and Barkley, but the goal was ruled offside following a VAR check.
VAR then had a look at a possible penalty for a Chilwell handball, but it clearly struck the defender's back and play continued after an eventful few minutes in Portugal.
Kane struck just wide of the Netherlands post in the 90th minute before the match headed for seven additional minutes, which saw Lingard also just miss the Dutch goal with a curling effort.
Depay had a golden chance to win it for Koeman's side in the final moments after Bergwijn had got the better of Maguire, but the former United attacker blazed over the crossbar from close range. Sterling then kissed the top of the Netherlands goal with a curling attempt as both teams had huge chances late on.
Kane had to clear a Virgil van Dijk header off the line as Netherlands made a strong start to extra time.
However, it was a horror mistake from Stones that led to Koeman's side scoring a second - Depay saw his effort saved by Pickford after the mistake from the City centre-back. However, Promes was on hand to bundle the ball home off the boot of Walker, who was credited with the own goal.
Depay and Van Dijk had chances to score a third for Netherlands in the period that followed with England struggling to deal with the pressure.
Eventually Netherlands wrapped up their spot in the final in the 114th minute when another mistake, this time from Barkley, led to Depay squaring for Promes, who simply could not pass up the chance to make it 3-1 on a fine night for the team in orange.
NETHERLANDS (4-3-3): Cillessen; Dumfries, De Ligt, Van Dijk, Blind; De Roon (De Beek 68'), Wijnaldum, F De Jong (Strootman 114'); Bergwijn (Propper 91'), Memphis, Babel (Promes 68')
ENGLAND (4-3-3): Pickford; Walker, Stones, Maguire, Chilwell; Delph (Henderson 77'), Rice (Alli 106'), Barkley; Sterling, Rashford (Kane 46'), Sancho (Lingard 61') body check tags ::