Benzema scored a double at the Santiago Bernabeu on Sunday night but Barca claimed a 4-3 victory in a pulsating match.
Andres Iniesta put Barca ahead just four minutes in but Benzema's brace turned it around before Lionel Messi levelled before the break. Cristiano Ronaldo's penalty restored Madrid's lead but, after Sergio Ramos brought down Neymar in the area, Madrid were down to 10 and two Messi penalties won it for the visitors.
The result means the title race with wide open, with Real level on points with leaders Atletico Madrid and Barca only one point back.
Benzema told the club's official website: "We're disappointed with the result. We scored three goals and had control of the game.
"When Barcelona don't have it, it is very difficult for them and we played a great game. Barcelona always have possession and we adapted our game against that team and we were doing well.
"I scored two goals but it doesn't matter, the important thing is the result.
"I do not know if it was a penalty from Sergio on Neymar and after the red it is very difficult playing against 11 men.
"It was a night with a lot of key moments and now we'll try and beat Sevilla. At this point in the season the matches are all finals and we know that Atletico take on Barcelona on the final day, so we have to think about ourselves in order to win."
Real defender Marcelo also believes the sending off was a turning point in the match.
He said: "We fought hard but it is difficult when you are a man down. We'll look at our mistakes in order not to make the same errors again.
"We can hold our heads high, there are still a lot of matches to play. If we had beaten Barcelona it would not have been the end of La Liga and we knew they were a great team.
"We tried to do what the coach asked of us. You cannot play well in every match and the defence will not always keep a clean sheet.
"I'm not going to speak about the referee because there's no need. It made it difficult playing with a man down, but there is still a lot of league to play.
"We are going to try and get a victory away to Sevilla. We have to see what our errors were so that we don't repeat them, it's another game, another final and we have to win no matter what."