The 40-year-old coach was happy that his side were able to take one point from such a difficult trip and stressed he had no reason to complain about the refereeing decisions
Madrid assistant coach Aitor Karanka was unhappy with the refereeing decisions in the match, but Emery had a different opinion regarding the officials' work.
"I think the referee did well," Emery told reporters after the match. "I do not think he had any influence on the result."
"Playing at the Bernabeu is always hard and Madrid had come off a good run and were very strong. In order to get something out of this match, we knew we had to take it in a direction in which we could follow our plan, have possession of the ball, have faith in attack, create chances to score and have a bit of luck.
"We had two clear chances to score and we are satisfied because we have the feeling that we were solid and we can win things. We didn't let Madrid pass the ball easily and stopped them countering. We had bits of luck, but at all times we felt we could win.
"We leave with one point, which is a reason to be happy, considering we were playing at the Bernabeu. We wanted the victory, but the draw also leaves us somewhat satisfied."
It was Valencia's fourth consecutive winless match, but Emery is confident that the draw against the Liga leaders comes as a huge boost to his men.
"We were able to get a point, something that only a few [teams] can do, and this will boost our self-esteem," the 40-year-old said.
"There are not many matches left and there is a lot at stake for us.
"We need some of the players who have not been playing well to produce more and we will need to continue to develop some of the positive things we did today."
Valencia resume La Liga action on Wednesday when they host Rayo Vallecano.