The 25-year-old was visibly angered by manager Xabi Alonso's decision to pull him off in the 72nd minute for fellow countryman Rodrygo, storming off straight to the changeroom in disdain.
According to ESPN, Vinicius was due to meet with his head coach to discuss the issue on Wednesday morning following a two-day break, with the player issuing a statement on his X account.
"Today I want to apologise to all Madrid fans for my reaction to being substituted in El Clásico," stated the Brazilian.
"Just as I did in person during today's training session, I also want to apologise again to my teammates, the club, and the president.
"Sometimes my passion gets the better of me; 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.
"I promise to keep fighting every second for the good of Real Madrid, as I have done since day one."
Vini has scored five goals and provided four assists in La Liga this season but is yet to open his account in the UEFA Champions League.
The top of the table Los Blancos will take on 18th placed Valencia next at the Santiago Bernabeu on Saturday.
Liverpool manager Andoni Iraola has warned Bradley Barcola that he must learn to handle the pressure and scrutiny that come with his reported 123 million pounds transfer from Paris Saint-Germain.
Inter Milan captain Lautaro Martinez is facing around a month out of action after suffering a hamstring injury, dealing a major blow to the Serie A leaders.
Manchester United defender Lisandro Martinez has admitted that anger and frustration after the 2-0 Champions League defeat to Atletico Madrid prompted his criticism of the club's transfer strategy.
Deniz Undav ended his goalscoring drought as VfB Stuttgart beat Slovan Bratislava 3-0 in the Champions League on Wednesday, insisting that team success matters more than his personal statistics.
