The Red Devils came from behind to secure their place in the quarter-finals of the Europa League on Thursday night.
Dorgu starred on the left flank for Ruben Amorim's side and was a constant attacking threat for the hosts.
His runs into the penalty area appeared to be too much for substitute Hamari Traore.
As the United full-back ran towards the goal-line, Traore slid in to bring Dorgu down.
Referee Benoit Bastien immediately pointed to the spot, awarding a penalty for the fourth time in the match.
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However, replays appeared to show Traore had won the ball before making contact with his opponent.
Although a VAR review took place, Bastien reversed his decision without going to the pitchside monitor or making the VAR gesture on the field.
Instead, the ball was handed back to the visitors with play restarted.
Replays went on to show Dorgu had approached the official to tell him it was not a penalty.
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Footage of the incident appeared to show the Danish defender saying: "It's not a penalty."
Supporters were quick to praise the 20-year-old on social media for his response to the decision.
Commenting on the incident, one fan wrote: "It's a shame this kind of thing is so rare in football, brilliant sportsmanship."
Another added: "Refreshing to see."
Meanwhile, one more said: "Great sportsmanship, great kid."
United had already turned the match around to lead both on the night and on aggregate.
Following a 1-1 draw in Spain last week, Sociedad took the lead after ten minutes thanks to a penalty from Mikel Oyarzabal.
Bruno Fernandes levelled after United were awarded a spot-kick of their own six minutes later, though.
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Another penalty shortly after the start of the second half saw the home side take the lead before Fernandes completed his hat-trick late on.
Diogo Dalot went on to add a fourth and cap off a brilliant performance in stoppage time.
United will now face Lyon next month for a place in the semi-finals.