United were beaten 2-1 at Old Trafford to go down 3-2 on aggregate after Nani was sent off early in the second half for what was a very questionable call.
Sergio Ramos' own-goal had allowed United to take the lead just after the break but the red card turned the tide of the contest with Luka Modric and Cristiano Ronaldo sending Madrid through to the quarter-finals at the expense of a heart-broken United side.
"It's a distraught dressing room and a distraught manager," said Phelan. "That's why I'm sat here now (and not Sir Alex Ferguson).
"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 (red card) 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."