After the game, when Koeman tried to leave the stadium in his car, a number of people surrounded and slapped the vehicle as the Barca coach edged forward until getting away.
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The club released a statement on social media that read: "FC Barcelona publicly condemns the violent and disdainful acts that our manager experienced when leaving the Camp Nou.
"The club will take security and disciplinary measures so that such unfortunate events do not happen again."
There were no crowd restrictions for the first time since the COVID-19 pandemic, and the Camp Nou welcomed back 86,000 supporters for El Clasico.
Sergio Aguero's first goal for Barca proved to be a consolation as they sit ninth in the LaLiga table, with 15 points from nine matches, six points behind leaders Real Sociedad, who have played an additional game.
Koeman has come under scrutiny in the wake of the team's mediocre results, leading to speculation over his future at the club.
Information from The Associated Press and Reuters was included in this report.