Vinicius reacted furiously when substituted by coach Xabi Alonso on 72 minutes with Real leading Barcelona 2-1 on the night.
The Brazil attacker refused to acknowledge Xabi when crossing the touchline and stormed down the players' race for the home dressing room.
He was later convinced to return to the dugout, though his behaviour has since been slammed by pundits.
Now, Vini Jr has made a statement apologising for his actions - though significantly did not include Xabi in his apology.
It read: "Today I want to apologise to all Madrid fans for my reaction when I was substituted during the Clásico.
"As I did in person in training today, I want to reiterate my apologies to my teammates, the club, and the president.
"Sometimes passion and the desire to win take over. My character is born from the love I feel for this club and everything it represents. I promise to continue fighting every second for the good of Real Madrid, as I have done since day one."