The home side lost 2-1 at Wembley in their opening UEFA Nations League match.
England lost full-back Luke Shaw early in the second half when he collided with Spain's Dani Carvajal, but they rallied late in the second-half and nearly equalised when Kane put Rashford through for a shot that De Gea blocked with his legs.
Rodrigo Moreno then took advantage of poor marking at a free-kick to score the victor from close range after 32 minutes.
Kane, who scored six goals in seven games, was presented with the award by England manager Gareth Southgate before kick-off. At the moment we have a different profile of player, we can't play the way that they want to play.
England's first worldwide match since their run to the World Cup semi-final at the World Cup earlier this summer ended in defeat, with Gareth Southgate's young side slipping to a 2-1 loss to Spain tonight at Wembley.
Kane rages at ref as Spain puncture England’s feel-good factor
Rashford would have had a second ten minutes before the break but for a stunning reaction save from his Manchester United team-mate De Gea.
'Going by numbers and performances, he is world's number one'.
However, the United 'keeper produced the sort of stunning save he does routinely at club level to deny Rashford an instant equaliser with a powerful header from point-blank range.
"I've seen teams fold in that sort of situation, but we finished really strongly, created a couple of very good chances, have probably had as many shots on target as they have". Caught in a completely innocuous collision with Spain's Dani Carvajal, Shaw looked to be in some distress as he was forced from the pitch prematurely.
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