Real won 3-1 at the Nou Camp with a Sergio Ramos penalty, awarded via VAR, the flashpoint.
"It was a really tough match," Dest said. "We had chances, they had chances, and it's just too bad that we lost.
"It's my first El Clasico and I'm just p***ed that we lost.
"They were maybe a little bit sharper in the chances. They finished them and we didn't.
"We have another game on Wednesday against Juventus [in the Champions League] and we have to win that one and get the team spirit back."
Ronald Koeman placed Dest in his natural position at right-back and the American put together a decent performance, both defensively and in attack.
Asked where he prefers to play, he stressed that he can feature wherever he is needed.
"I feel a little more comfortable on the right, but if I have to play on the left, that's no problem for me," Dest stated.