Vinicius refused to acknowledge Xabi as he left the field and stormed towards the home dressing room, but eventually returned to the dugout.
His actions were criticized by commentators after the game.
Vinicius has since released a statement apologizing for his reaction, but it does not specifically mention Xabi.
In the statement, Vinicius said, "I want to apologize to all Madrid fans for my reaction when I was substituted during the Clasico."
"I also want to reiterate my apologies to my teammates, the club, and the president," he continued.
"Sometimes, passion and the desire to win can get the best of me. My character is driven by my love for the club and everything it represents. I promise to continue fighting for the good of Real Madrid, as I have since day one."
