The 25-year-old Brazil international did not play in Real's 3-0 win the semi-final first leg at the Bernabeu, but was seemingly subjected to monkey chants from the away supporters as he warmed down after the game with his young son by his side.
Marcelo posted on Twitter on Thursday evening: "I want to thank all of you for the support you have given me today.
"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."
Reports suggested the full-back was labelled a 'monkey' by the Atletico fans who remained in the virtually empty stadium after full-time, and when Marcelo's young son ran out to hug the player they changed their tune to 'May your father die'.