England's Nations League campaign opened with defeat as they were beaten by Spain in their first match since reaching the World Cup semi-finals.
Marcus Rashford gave England the perfect start with an 11th-minute strike from Luke Shaw's pass but Spain responded with an almost instant equaliser thanks to Saul Niguez's low finish.
Rodrigo Moreno then took advantage of poor marking at a free-kick to score the winner from close range after 32 minutes.
England suffered a blow just after half-time when Shaw was taken off on a stretcher with a head injury following an accidental collision with Dani Carvajal but they rallied late on and could have earned a draw.
De Gea, who saved brilliantly from Rashford's header in the first half, denied his Manchester United colleague once more and England were furious Dutch referee Danny Makkelie ruled out an injury-time finish from substitute Danny Welbeck after Spain's keeper tumbled under pressure from the striker.
England were left to ponder their first competitive defeat at Wembley since they lost a Euro 2008 qualifier to Croatia in November 2007, a run stretching back 24 games - and also Southgate's first home defeat as manager.