The Brazilian was withdrawn in the 71st minute and replaced by compatriot Rodrygo, despite having played a key part in the winning goal and running Barcelona's right back Jules Kounde ragged during the fiery encounter.
Vinicius made his displeasure known to manager Xabi Alonso before heading directly to the dressing room, casting a shadow over what should have been a celebratory moment as Real ended a four-game losing streak against their bitter rivals.
While Vinicius revealed he had personally apologised to his teammates and club president Florentino Perez, notably absent from his statement was any mention of Alonso.
"Today I want to apologise to all Real Madrid fans for my reaction when I was substituted in El Clasico," Vinicius said via his social media accounts. "As I have already done in person during today's training session, I also want to apologise again to my teammates, the club and the president."
The 25-year-old attributed his outburst to his competitive drive, explaining: "Sometimes my passion gets the better of me because I always want to win and help my team. My competitive nature stems from the love I feel for this club and everything it represents."
Vinicius has had a testy relationship with Alonso since he took over as manager in May. Alonso has substituted him in most games this season, even though Vinicius has been linking up well with forward Kylian Mbappe.
But even after storming off the pitch, his part in a testy match was not over. He reemerged just before the final whistle after Pedri was sent off, and a fight broke out between the teams. He had to be shepherded away from the scene as he argued with Barca players.
Real have 27 points at the top of the LaLiga standings, five ahead of Barcelona in second.