United appeared to be in control of the second leg of the last-16 tie when Nani's low cross early in the second half was turned into his own net by Sergio Ramos.
However, Nani was then shown a red card for catching Alvaro Arbeloa before goals from Luka Modric and United old boy Cristiano Ronaldo sent Real through 3-2 on aggregate.
Assistant Mike Phelan attended the post-match press conference in place of Sir Alex Ferguson and explained the United boss was not in 'any fit state' to speak to Turkish referee Cuneyt Cakir about the sending off.
"It's a distraught dressing room and a distraught manager," said Phelan. "That's why I'm sat here now.
"We thought we had the tactics right for the game for such a big occasion. We felt comfortable at times and 0-0 was where we wanted to be.
"We came out, scored a goal and that put us in a commanding position. Then the game totally changed.
"The decision was amazing, but we had to carry on. Playing Real Madrid with 11 men is very difficult and, in a game of this magnitude with all the world watching, we feel very, very disappointed that we ended the game with 10 men.
"I don't think the manager is any fit state to talk to the referee about the decision.
"I think it speaks volumes that I'm sat here speaking to you at this moment in time and not the manager of this fantastic football club.
"We all saw and witnessed a decision that seemed very harsh, possibly incredible, at that moment in the game."
The pre-match talk was dominated by Ferguson's decision to leave Wayne Rooney out of the starting line-up but opposite number Jose Mourinho defended the decision.
Rooney was left kicking his heels on the bench for the first 70 minutes of the 2-1 reverse and was only introduced once the Red Devils had fallen behind.
"Sir Alex has won the right for every decision to be correct and never have a question mark against them," said Mourinho. "He is the best. He is the top.
"You (reporter) are nobody to put a question like that. I am nobody.
"He did a great job."
It is hard to argue Ferguson got the call right given the two men who profited most from Rooney's omission, Ryan Giggs and Danny Welbeck, were two of United's better performers.
Nevertheless, there is now bound to be speculation over the England man's future.
The last time Real Madrid came to Old Trafford, Ferguson left out David Beckham.
And though - like Rooney - the midfielder was eventually introduced, he left United that summer.
The next move is awaited with interest, particularly as United now have a tough FA Cup quarter-final to prepare for against Chelsea on Sunday.
"The decision was tactical," added Phelan. "In that dressing room, everyone was fit.
"But big decisions have to be made. Tonight we had the balance just right."