Raphinha struck twice on Sunday as Barca won 4-3 at Montjuic.
He said afterwards: "We knew the importance of the Clásico. We had to stay calm to turn it around (after going 0-2 down).
"It's hard to imagine a lot of goals in a Clásico. The way both teams play can lead to that. Anything can happen. The important thing is knowing how to defend in the key moments.
"Given the chances we missed, maybe (we suffered more than expected). Real Madrid's third goal made things more difficult. But we were able to defend well."
On his brace, Raphinha said: "I could have scored more. I missed three chances that I can't afford to miss. I have very high expectations of myself. I think more about the ones I missed than the goals I scored. But I'm happy to be helping the team.
"It's all up to us. We have to celebrate today's victory. The Clásicos are very important. But we have to win one more game."
On being named man-of-the-match, he also insisted: "I'd give it to other players before me. I haven't had my best game. To Lamine Yamal, to Szczesny, Cubarsí, Iñigo... Or Pedri, who for me is always the MVP. I've been below them."