Barca won thanks to a stunning volley from Zlatan Ibrahimovic on 56 minutes.
But Pellegrini declared at the final whistle: "I am evidently not very satisfied. I never enjoy losing, but I am pleased with the way we played.
"We had possession and knew what we wanted to do in attack. We had many chances, but we weren't patient enough when it came time to finish. Unfortunately the match came down to one single play.
"We know how Barcelona like to play. They want to hold onto the ball, but they were up against a Real Madrid that was better than them in many facets of the game. I think we at least deserved a draw. We had more chances than they did, especially in the first half. They scored in the second half, but we also had our opportunities.
"I don't think the team were deflated. We were very physical, which is why Barcelona had trouble when they had the ball. What happened towards the end was a result of us not finishing the way we should have and relying on long balls to attack in a more direct manner.
"Cristiano Ronaldo could only play a maximum of 60 minutes. Had he played more would have been rash. I think he played all he could and that we made the right changes. Regarding Higuain and Benzema, both had the chance to help the team. Pipa started because he has been in great form of late."