England's defeat was their first in their last 25 competitive fixtures at Wembley.
England reached the semi-finals in Russian Federation, but lost to Croatia and then fell to Belgium in the third-place game.
In the past Spain were vulnerable whenever they lost possession but against England they seemed more comfortable without the ball and defending with their backs against the wall, as they had to do in the latter stages of the game.
The Manchester United man has been in great form for United this season and earned a spot back in the England side.
"In the second half we knew how to cope under pressure and that's an important thing for us, that we stuck together in tough moments like in the second half".
Luke Shaw, making his first worldwide start in three years, was taken off on a stretcher wearing a neck brace and oxygen mask early in the second half after a clash with Dani Carvajal, and the hosts failed to mount a comeback in his absence.
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The singer and Spain X Factor judge has been going out with De Gea for six years and has constantly supported him in public, particularly on social media.
"That balance with the left footer for us, with him and Danny (Rose), was an advantage in several situations".
The Three Lions came close to equalising in injury time after De Dea dropped the ball on Welbeck before the Arsenal forward finished from close range.
"We need to asses over the weekend, but I think it's likely we'll need to call some players in", Southgate said.
"It takes time. We've come a long way in a short space of time and today was as tough a test as you could have against a team that presses like that and are so good in possession".
There was much to ponder for Southgate who has now seen his side lose three matches in a row against Croatia, Belgium and now Spain - proof they are still a work in progress.