Emery's men went down 2-1 at the Santiago Bernabeu on Wednesday, with James Rodriguez and Jese's goals enough for the hosts despite Iago Aspas' late goal for the visitors.
Still occupying fourth spot after the defeat, Sevilla could have moved within two points of third-placed Atletico Madrid with a victory - something Emery said was hard to achieve, due to referee Ignacio Iglesias.
Injury to insult was Beto's substitution out of the game in the 35th minute with a suspected serious head injury, but Emery said the custodian's trip to hospital was mere precaution.
"It's hard to play Madrid at the Santiago Bernabeu. The one thing which makes me most proud is that we competed for 90 minutes," he said after the game.
"Even at 2-0 down, we were patient and created chances. We can safely say that we deserved something more.
"Of course, we're not satisfied because the defeat is above everything. I'm very proud of all the players.
"Real Madrid were very efficient in the first half, but [substitute goalkeeper] Sergio Rico had a great game. My only satisfaction is our teamwork.
"Madrid were both individually and collectively very good, even against rivals like ourselves.
"They've recovered and know how to suffer. [Our goal] came about too late for us to get the draw.
"With Beto, there's no need to panic. He'll undergo tests but went to hospital as a precaution."
Emery said defensive midfielder Vicente Iborra performed admirably, especially in attack, despite missing from point-blank range in the 59th minute.
"Iborra's a productive player. He's played in more advanced positions before as he can be quite dangerous in the box," the coach continued.
"He had a great game and has a very good attitude but lacked a goal.
"Football is a contact sport. At Real Madrid, when you don't have contact with their players, they dance past you.
"It wasn't a brutal match but competitive and intense. It's a very difficult game and pitch for the referee. We lost the points because of him [Iglesias]."
