After taking the lead at Wembley through Marcus Rashford's early goal, England were undone by strikes from Saul Niguez and Rodrigo Moreno as Spain's midfield began to control the game.
De Gea had been labelled as one of the main culprits for Spain's poor showing in being knocked out by the hosts at the last 16 in Russian Federation as he made just one save in the whole competition.
Asked if the goal should have stood, the England striker told Sky Sports Football: "Yeah, 100 per cent".
He said: "In those big moments you need the ref to stay strong, and unfortunately he's bottled it".
Then, though, came a stirring climax that Danny Welbeck thought he had capped with a dramatic 97th-minute equaliser when finishing from an acute angle after De Gea had dropped the ball.
"There's a lot of stuff we can learn from, but I think we can hold our heads up high".
Today was a tough test in terms of pressing and a team who are so good in possession.
Southgate echoed his captain's frustration but did not allow the official's mistake to mask some of England's shortcomings.
Fiji: magnitude 7.8 quake rocks coast
Pacific Tsunami Warning Centre messages do not represent the official warning status for New Zealand. The USGS said only "light" shaking would have been felt across the Pacific Ocean archipelago ocean.
Most notable was Gomez's forward passing, with the Liverpool defender showcasing a rare ability, or perhaps willingness, to play vertically rather than horizontally.
"I think it's clear for everybody to see that it should have been a goal".
"We are under no illusion that Spain were the better team for long periods. There are individual positives and as a collective they gave everything", Southgate said of the trio who were given their chance to make their mark.
"Their retention of the ball was top class".
"We'll have to assess him a little bit more overnight but that's definitely a good sign".
"But even when you press well against them, they have some wonderful players that can wriggle out of problems and play first time out of situations".
"At the moment, we're not able to do that when teams are pressing us high".
"He may be making mistakes like everyone else, but we have one of the best in the world, and I'm very calm with David".
"Paul Gascoigne, Steven Gerrard, Paul Scholes, we've had players like that in the past".