United felt the decision, made by a UEFA technical panel at the game, was insensitive given the role the Mexico international defender played in the appalling injury to Shaw.
A source at the Old Trafford giants said: “We found it strange and disappointing that UEFA made him their man of the match after what happened to Luke.”
Medical staff are optimistic the 20-year-old will miss only six months, with left-back Shaw believed to have suffered a “clean break” in the incident.
A United statement on Wednesday read: “Luke underwent surgery for his injury last night and will remain in hospital in Eindhoven to continue his early recovery.
“Manchester United are grateful for the excellent care he is receiving and would like to thank everyone who has sent messages of support. A further update will be provided in due course.”
Moreno, who scored PSV’s equaliser on the night after the Shaw incident, protested his innocence over the challenge and said he empathised with the crocked United man — having suffered a similar injury himself during last year’s World Cup.
“I just feel really bad because I was involved in the accident,” said the 27-year-old. “I feel really sorry. I think I played the ball, but in this kind of situation I don’t care if it was a foul. I feel bad for him, for his family.
“I had myself a situation like that during the World Cup and it’s bad. It’s difficult to say what happened. I just hope he will be back as soon as possible.”
Daley Blind said he and his United team-mates were left distraught by Shaw’s injury and feels it had a bearing on their defeat.
Louis van Gaal‘s side scored in the aftermath of Shaw’s injury, but folded as PSV netted twice to beat them on their Champions League return after missing the competition last season.
Blind admitted Shaw’s injury took a mental and emotional toll on United’s players.
He said: “It’s something you may not actually be influenced by at that time. But you can be unaware, perhaps in your head, that you subconsciously sympathize with him. But it’s a defeat, and saying this should not pass the buck. It’s a massive blow if such person incurs an injury.
Luke Shaw’s injury in pictures (warning — graphic content):
“We are a strong team unit, so it cuts into you. Maybe it gets into your heads, but you have to let it pass. We played well in the first half. We created many chances and had the opportunities to decide the game, but failed to finish it.”
Shaw’s long-term absence means a selection headache for Van Gaal.
Blind and Chris Smalling had formed an effective central defensive partnership in the early weeks of this season.
But Van Gaal may have to break them up, with Blind moving to left-back and Marcos Rojo, who came on for Shaw in his first appearance of the season, partnering Smalling in central defence.