Adan was chosen ahead of Iker Casillas for the second consecutive game, but was sent off after just six minutes.
"It was an unfortunate bit of play where the referee blew for a penalty and the sending-off seems unfair to me," he said.
"These things happen and you have to accept it and push forward. This can happen, you can come away having played a perfect match and having made big saves or you can come away having been sent off. The important thing is what has led me to being in goal for Real Madrid has been my hard work."