The center back was also booed by the England fans following his role in the Champions League final.
Even during their morale-boosting run in Russian Federation, manager Southgate warned there was still work to do and the performance at Wembley underlined that message.
The Three Lions took an early lead in the 11th minute after Luke Shaw found Marcus Rashford, with a defense-splitting pass, with the latter making no mistake in slotting the ball past his club teammate to give his nation the lead.
Southgate's team included the returning Luke Shaw and Joe Gomez, with both players impressing as Shaw set up Rashford's opener and Gomez looking composed throughout.
"I think we've got some players who can and have shown tonight they can perform at that level, and there's some that are still a work in progress", he said.
Meanwhile, England have called up Leicester City duo Ben Chilwell and Demarai Gray for Tuesday's friendly against Switzerland at the King Power Stadium, the FA said on Sunday.
Djokovic overcomes dogged Millman to reach semis
Keys won all 10 of her service games, saving the only two break points she faced. Just an all-around player. "He made me run and he made me earn my match today".
Southgate is planning on rotating his squad and Spurs left-back Danny Rose is expected to replace Shaw down that flank.
Tottenham full-back Kieran Trippier said there was no reason for alarm despite the defeat, which follows losses to Croatia in the last four in Russian Federation and to Belgium in the third-place play-off.
Spanish singer Edurne, girlfriend of Manchester United and Spain goalkeeper, David De Gea turned to social media to congratulate her partner for his performance in Spain's 1-2 win over England at Wembley on Saturday night in the Uefa Nations League.
"It is not a concern", he said. At times his previous goals have come outside the box and we know he can hit the ball. He remains someone with a detailed knowledge and understanding of English players across the senior and junior ranks, a detailed knowledge and understanding of the FA too, and a coach with an ambitious vision for England as a major global force. We can either go back to our old style and we'll never be a top team, or we can keep trying to do what we do and suffer at times.
"This was a ideal night, the team picked up a huge victory and we saw a very impressive Spain side", said Saul.