The decision comes after United were cruelly knocked out 2-1 by the Spanish champions after Nani was given a controversial red card in the 56th minute.
The Red Devils were leading 1-0 at that time, but after being reduced to 10 men, they would go on to lose the match and be eliminated as a result.
BBC Sport reported the following:
The Guardian's Daniel Taylor reports that manager Sir Alex Ferguson was too distraught to attend the press conference himself, sending assistant manager Mike Phelan to answer questions in his stead.
Referee Cuneyt Cakir is sure to draw plenty of differing opinions about penalty, which completely changed the flow of this Champions League contest.
As The Independent's Sam Wallace highlights, Nani's kick shouldn't have drawn a red card by definition, especially given the fact that he did not see Madrid's Alvaro Arbeloa before they collided.
TSN soccer analyst Jason deVos was in agreement.
The decision not to talk to the media is a smart move by both Ferguson and the United players, despite the fact it will draw criticism in the present.
Airing out their anger and frustation behind closed doors makes far more sense than openly criticizing the referee, perhaps saying things they will later regret.
The Red Devils should be commended, if not praised, for rising above a situation they have every right to be furious about. It's a classy move, and one that speaks to the team's mental fortitude.
In the end, United can only blame themselves for allowing two goals after the red card. They had to defend and hold out against Madrid, and they could not do so.
Champion teams find a way to win in the face of adversity, and United came up short.