Cakir caused uproar when he showed Nani a red card following a collision with Alvaro Arbeloa, prompting Real to turn a 1-0 deficit into a 2-1 win.
However, the referee has remained defiant, telling Spanish newspaper As: "I feel good and I do not doubt my decisions. Nani's red was correct. The world will realise the truth over time."
Cakir also defended previous red cards shown to players from English clubs; Chelsea's John Terry and Gary Cahill, and Manchester City's Mario Balotelli.
He said: "In the previous games with the English teams there was no unfair decision.
"What decision was incorrect? The red to Terry or Balotelli? I don't think I made a mistake in showing those cards and sending them off."
UEFA also backed the controversial official. Their assessor, refereeing legend Pierluigi Collina, awarded Cakir a mark of 8.2 out of 10.
He reportedly said in his report that Cakir's only mistake was in not sending off Rio Ferdinand who sarcastically applauded the 36-year-old after the final whistle.
United's players angrily surrounded the official after the final whistle, while Sir Alex Ferguson pulled out of his post-match press conference as his assistant Mike Phelan said he was "in no fit state" to face the media.
On Friday morning, Ferguson said of the dismissal: "It is hard to keep your faith when you have things like that. That’s the third time we have been knocked out by a referee."
Cakir said of the controversy: "It doesn’t make me very sad, I just don’t think about it.
"I have received more criticism on previous occasions, but I have always got back up and come back.
"I can do so again. I try to do my job correctly and I am doing well. I need to continue like this. I do my job perfectly."