Isco was whistled by supporters in the Santiago Bernabeu as Real Madrid lost to CSKA Moscow 3-0, their worst home loss in Champions League history.
The Spanish midfielder, who has struggled under Santiago Solari, also rejected the captain's armband from Marcelo.
Marcelo, who started the match as captain, was subbed off and "tried to give the armband to Isco. But he told me that I had to give it to Carvajal. I don't know what the reason for that was."