Videos on social media appear to show Barca's Lamine Yamal being subjected to taunts by a section of home fans as he celebrated his 77th-minute goal by pointing to his name on the back of his shirt.
Robert Lewandowski scored twice and Raphinha completed the scoring as the visitors cruised to a win that takes them six points above their rivals at the top of LaLiga.
Real Madrid did not specify which players had been subject to what they called "deplorable and despicable insults" as they opened an investigation into the matter, but Vinicius later referenced Yamal, Raphinha and Ansu Fati in his own statement on social media.
"It's regrettable what happened yesterday at the Bernabeu with racist insults," Vinicius wrote on X.
"There is no place for these criminals in our society. All my support to Lamine, Ansu and Raphinha.
"I know that Madrid and the police will do things to identify and punish the guilty!!"
In June this year, Vinicius said he is a "tormentor of racists" after three Valencia fans were sentenced to eight months in prison for abusing him during a LaLiga game at Valencia's Mestalla Stadium on May 21, 2023.
A Real Madrid statement on Saturday's incident read: "Real Madrid strongly condemns any kind of behaviour involving racism, xenophobia or violence in football and sport, and deeply regrets the insults that a few fans uttered last night in one of the corners of the stadium.
"Real Madrid has opened an investigation in order to locate and identify the perpetrators of these deplorable and despicable insults so that the appropriate disciplinary and judicial measures can be taken."
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