Bidding to join Portugal in the final of the inaugural edition of the tournament, England enjoyed a perfect start when Marcus Rashford put them ahead from the penalty spot.
But the Oranje fought back through Matthijs de Ligt's equaliser before netting twice in extra time to seal a 3-1 win and move forward into the decider.
Stones was at fault for two of Netherlands' goals in extra-time after being caught in possession well inside his own half; but Southgate refused to condemn the Manchester City star for his lapses in concentration.
"It’s easy to turn round and kill them," the manager said after the final whistle on Thursday. "But we have some defenders who are prepared to take the ball in areas where many defenders in the world aren’t, and it’s been the bedrock of how we’ve progressed. We have to continue it but of course we can’t continue to make the mistakes we did."
On Stones, Southgate said: "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.
"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 tonight."
The 25-year-old did indeed fall out of favour with Pep Guardiola towards the end of the season, starting just three times from March onwards as City took a domestic treble.
And Southgate admitted that if he continued to be left out of the starting line-up his England place may come under review.
"I think we have to wait and see how that develops," he added.
"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."
Asked about alternatives to Stones in the Netherlands contest, Southgate dismissed Joe Gomez, noting he had just arrived from the Champions League final with Liverpool, and claimed Michael Keane did not have big-match experience yet.
"He hasn’t played in this sort of game," Southgate said of Keane. "I think Stones and Harry Maguire are our best two, and I have got to be there to support them in their difficult moments."
Stones has appeared 38 times for England to date, scoring two goals and representing his nation at the 2018 World Cup.