Young went down in the second half to win United a penalty, but as it turned out, Robin van Persie missed it anyway.
However, former United captain Roy Keane was scathing in his analysis on ITV, claiming Young had "conned" Italian referee Nicola Rizzoli, who booked Markel Bergara for the challenge.
Moyes adopted a more defensive tone.
"I have seen it and the boy certainly tugs him in the box," said the United boss.
"If you look the referee is two yards away from it and decided to give it.
"All I know is he got a penalty kick from a decision, I don't know anything about reputations or anything.
"The referee was there. He made quite a lot of decisions tonight and that one he gave a penalty kick."
Sociedad coach Jagoba Arrasate was less certain.
"I couldn't really see it from the dug-out," he said.
"The player kind of folds. I would need to see all the replays from the TV."
Young was also castigated by Sky Sports pundit Ray Wilkins.
"This is pathetic," Wilkins said. "This is as bad for me as all these over-the-top tackles we're getting at the moment because that is a conning of the referee.
"I just wish Ashley would cut this out because he's a good player but he's getting a bad name."
That Van Persie missed probably took some of the heat out of the situation, with the eventual 0-0 scoreline meaning United will advance to the knockout stage if they win one of their remaining two fixtures.
Wayne Rooney backed his fellow striker to bounce back from his spot-kick failure, saying: "Of course [everyone misses from time to time].
"Most forwards in the world miss penalties.
"That won't affect him, I'm sure."
United will be without Marouane Fellaini when they visit Bayer Leverkusen in three weeks' time after the Belgian was sent off in stoppage time for two yellow card offences.
"As I said earlier regarding the penalty kick the referee made decisions all night," said Moyes.
"He is the one who must have seen fit both to award a penalty and send a player off.
"I thought he made some strange decisions all night and that was another one of them."
The incidents took the heat off Javier Hernandez, whose failure to turn home Shinji Kagawa's second-half cross from six yards was inexplicable for a player of his undoubted class, who has scored three times in his last two games.
"The miss from Javier was an opportunity," said Moyes.
"To be fair to him the ball bobbled up. It just comes off the ground a little bit before it gets to him.
"But he gets in those positions week in week out and that is where he gets his goals from."