Carlo Ancelotti's men defeated local rivals Atletico Madrid 3-0 in the first-leg encounter, but it is alleged that some fans directed monkey chants and personal insults at the Brazilian as he warmed down.
Marcelo was an unused substitute in the match, but on Thursday claimed the abuse had taken place but that he had not been affected by it.
"I want to thank all of you for the support you have given me today," he wrote on Twitter. "And even though this is not the first time it happens I can promise you that we are stronger than any kind of racism.
"This will never affect me or my family."
Marcelo has made 25 appearances in all competitions for the Blancos this season.