Thursday's Nations League semi-final was poised at 1-1 in the first half of extra time when the 25-year-old was caught in possession on the edge of his own box.
Stones was robbed by Memphis Depay, who forced a save out of Jordan Pickford, but Kyle Walker bundled the ball into his own net under pressure from Quincy Promes.
The Netherlands went on to win 3-1 to set up a showdown with Portugal in the final, with Stones taking plenty of flak after the match.
But Southgate has leapt to the defence of the Manchester City man and has stuck by his decision to start him alongside Harry Maguire in Guimaraes.
"He knows I am here to support him. I know he is going to get criticism, but he's had a difficult end to the season in that he was not playing regularly at his club," Southgate told reporters.
"We still think he has been our best centre-back. He has huge qualities and huge potential to be a top player. But he has had so little football at the end of the season that the sharpness and fatigue as the game wore on were definitely factors in what has happened."
Stones has started four of England's five Nations League matches, but he appeared to fall out of favour under Pep Guardiola at club level towards the business end of the season.
And Southgate has suggested others could potentially usurp the former Everton defender should his situation not improve at the Etihad Stadium.
"I think we have to wait and see how that develops," he said. "At the beginning of the season he was playing in all the big games. That hasn't been the case towards the end but it was one of a number of difficult selection issues we had to deal with, really.
"But Joe [Gomez] was with us for only two days and he hasn't played either, and Michael Keane hasn't played in this sort of a game, so I think Stones and Maguire are our best two, and I have got to be there to support in their difficult moments."
England conclude their Nations League campaign with a third-place play-off against Switzerland on Sunday.