Just four places separate the two sides, but goals from Lionel Messi, Cesc Fabregas and Thiago Alcantara gave Tito Vilanova's side a 3-0 lead, before Diego Buonanotte struck an 89th minute consolation for the hosts.
"I felt like applauding Barca in the second-half," Demichelis told reporters after the game.
Despite the defeat, the Argentina international was keen to take the positives from the match and insisted the clash had brought the best out of Manuel Pellegrini's troops.
"When you make an error against Barca, it makes you focused again," he added.
"In the first half, we stood up to the best team in the world. We go home with our heads held high."
The Andalusians will have the opportunity to make amends for Sunday's loss when they travel to Camp Nou for the first leg of their Copa del Rey quarter-final on Wednesday evening.