Dest entered the history books as he became the first player from the United States to play in the well-documented fixture, featuring ahead of Sergi Roberto in defence.
"It was a really tough match, we had chances, they had chances," Dest said, according to BarcaBlaugranes.
"It's too bad that we lost. They were maybe a little sharper. They finished their chances. I'm pissed that we lost. It's my first Clasico and it's a nice game to play of course. But we have to keep going," he continued.
Barcelona were behind inside five minutes through Federico Valverde, but hit back through Ansu Fati before a controversial penalty from Sergio Ramos and a late finish from Luka Modric put the clash to bed.
A tough trip to Italy to face Juventus in the UEFA Champions League group stages on Wednesday lie and wait the Catalans, with a win non-negotiable.
"We must win the next couple of games now. We have Juventus next in the Champions League. We have to win that," the American pointed out.