Marcus Rashford’s penalty, awarded after he was fouled by Matthijs de Ligt, gave Gareth Southgate’s side an interval advantage.
De Ligt made amends when he took advantage of poor marking at a corner to power home a header with 17 minutes left.
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England thought substitute Jesse Lingard’s late strike had put them on course for the inaugural Nations League final against hosts Portugal in Porto on Sunday, only for VAR to intervene and rule it out for offside.
The Dutch were the far superior side but they were gifted their route to the showdown against Portugal on Sunday by suicidal defending in extra time by England, who were hoping to go one better than their World Cup semi-final exit against Croatia last summer.
England’s hopes of winning the Uefa Nations League are over after calamitous defending gifted the Netherlands a 3-1 semi-final, extra-time win here in Guimaraes.
Marcus Rashford had given Gareth Southgate’s side a 32nd-minute lead from the penalty spot before Matthijs De Ligt equalised with 17 minutes left.
England thought they had won it when substitute Jesse Lingard completed a wonderful team move with a cool 83rd-minute finish only for the goal to be ruled out for offside by the tightest of margins on Video Assistant Referee review.
John Stones was caught in possession by Memphis Depay who forced a brilliant save from Jordan Pickford, but Kyle Walker could only bundle the loose ball into his own net under challenge from Quincy Promes.