United exited the competition in controversial fashion, having led 1-0, 2-1 on aggregate, when Nani appeared to be harshly red carded, after which they conceded twice in quick succession.
Roared on by the home supporters, ten-man United poured forward as they hunted the two goals they needed to progress but visiting goalkeeper Diego Lopez managed to keep them at bay.
Ferdinand was upset after the match and sarcastically applauded referee Cuneyt Cakir before leaving the field.
And, writing on Twitter on Wednesday morning, the experienced centre-back said: "Morning, was a long night without any sleep.
"I must say last night our fans done us + our club proud. Best/loudest support I've heard at ANY ground throughout my career. Thank you."
None of Manchester United's players spoke to the media on Tuesday night after the 2-1 loss to Real Madrid, and manager Sir Alex Ferguson was 'too distraught' to take questions, according to assistant boss Mike Phelan.
"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," said Phelan.
"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.