Young went to ground theatrically during United's 0-0 draw in their UEFA Champions League Group A clash in Spain, earning a penalty that Robin van Persie could only strike against a post.
Replays showed minimal contact from Markel Bergara - who was booked for his apparent indiscretion - and Young was 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."
United boss Moyes warned Young about diving earlier this season but adopted a more defensive tone after the whistle in San Sebastian.
"I've seen it and the boy certainly tugs him in the box," the Scot said. "The referee is two yards away from it and decides to give it.
"All I know is he got a penalty kick from a decision; I don't know about his reputation, but the referee is there and he gave it.
"The referee made decisions all night. He's the one who saw fit to award a penalty and send a player off."
United's goalless draw has thrown Group A wide open, with Moyes' men now in a three-way tussle with Bayer Leverkusen and Shakhtar Donetsk to secure a place in the knockout stages.
United's next game in Europe sees them travel to Germany to tackle Leverkusen, before ending their Group A campaign with a home clash against Shakhtar.
And Moyes feels his side should be in a more comfortable position having missed a number of opportunities against Sociedad, with Javier Hernandez firing over from six yards out and Van Persie striking the post prior to his penalty miss.
He told Sky Sports: "It shouldn't have been a draw, it should have been a victory, we played well enough to win the game, made a lot of chances, and we missed a penalty as well.
"When you get opportunities you want to take them. Those opportunities tonight would have made sure we were well clear at the top of the group, but we're still in a good position.
"It's a good position, it's where we want to be, but we should have had three points tonight and made it a lot easier.
"We go to Leverkusen next and then we play Shakhtar Donetsk at home, so hopefully in those two games we'll make sure we qualify."
Moyes also saw midfielder Marouane Fellaini dismissed in the closing stages for a second yellow card and felt his side were not always favoured by referee Nicola Rizzoli.
He added: "I thought it was a difficult night all night for all the Manchester United players. They didn't get many decisions, but the referee has to do what he sees."