Los Blancos were 1-0 up thanks to Karim Benzema’s strike when the shot-stopper was given a straight red card for a foul in the penalty area.
The 25-year-old was chosen by Jose Mourinho to start ahead of captain Iker Casillas once again, and Adan believes that all the discussion in the last fortnight about the two keepers has been disrespectful.
"These past weeks many things have been said, but I’ve ignored them,” he told reporters after the victory. “It's 16 years since I came to this club and nothing really surprises me.
"There have been many disrespectful opinions about me and my job. I'm a cantera player. I know how I arrived here and I will keep on doing it my way.
"I was pissed off in the locker room [because] the red card was excessive."
Sociedad levelled from the spot after Adan’s dismissal, and Madrid required a Sami Khedira strike and two second-half goals from Cristiano Ronaldo to ensure victory at Santiago Bernabeu.
"The match started well, the team went out wanting to win at home and make the fans happy again, and we went ahead quickly,” the keeper added.
“After that everything got more complicated after the unfortunate incident, but the extra effort was appreciated when the team were playing with 10 men.
“The team were committed and pushed forward. I am sorry for [Jose] Callejon, who was sacrificed [brought off for Casillas] and is worse off in it all."