The game was stopped for almost 10 minutes during the second half at Mestalla, after Vinicius identified the fan in the crowd behind the Valencia goal.
Referee Ricardo De Burgos Bengoetxea activated Spanish football's anti-racism protocol, warning fans during the stoppage in play that any further racist comments would result in the game being suspended. Vinicius initially said he did not wish to continue playing but then decided to carry on after discussions with coach Carlo Ancelotti.
"It wasn't the first time, or the second, or the third. Racism is normal in La Liga," Vinicius posted on Instagram. "The competition thinks it's normal, the [Spanish Football] Federation does too, and opponents encourage it.
"I'm so sorry. The championship that once belonged to Ronaldinho, Ronaldo, Cristiano and Messi, today belongs to racists. A beautiful nation, which welcomed me and which I love, but which has agreed to export the image of a racist country to the world.
"I'm sorry for the Spaniards who don't agree, but today, in Brazil, Spain is known as a country of racists. And unfortunately, with everything that happens each week, I can't defend it. I agree. But I am strong and I will go to the end against the racists. Even if it's far from here."
The frustration for Vinicius has grown to the point that sources have told ESPN that his representatives have gone as far as to raise the possibility of the young star leaving the club due to the repeated instances of abuse.
The Brazil international is not currently considering leaving the club, sources said, but he is "at the limit" after repeated instances of of incidents involving opposition fans at a number of stadiums in recent months.
In a statement on Sunday, LaLiga said that it had "requested all the available images to investigate what happened" and that "once the investigation is concluded, in the event that a hate crime is identified, LaLiga will take the appropriate legal action."
Speaking to Movistar after the game, Ancelotti backed his player, saying that "LaLiga has a problem" with racism.
"I don't want to talk about football. I want to talk about what happened here. It's more important than a defeat," Ancelotti told Movistar. "What happened here today shouldn't happen. ... There's something bad happening in this league.
"[Vinicius] didn't want to continue. I told him it isn't fair that you have to stop the game. You're not responsible, you aren't the guilty one, you're the victim. And he carried on playing."
Vinicius was later sent off in the 97th minute after a clash with substitute Hugo Duro, and then sparked a confrontation with the Valencia bench with a gesture suggesting that Valencia were going to be relegated to the second division.
"It's a senseless red card because it wasn't aggression," Ancelotti said. "For me, Vinicius is the most important player in the world, the strongest player in the world. LaLiga has a problem. For me, with these racist incidents, they have to stop the game. Because it isn't one person. It's a stadium that insults a player. The game has to stop. I'd say the same if we were winning 3-0. There's no other way."
Vinicius has repeatedly suffered racist abuse from away fans in recent seasons, with LaLiga filing formal complaints after incidents at Mallorca, Real Valladolid, Atletico Madrid and Barcelona. The Brazil forward has said he feels insufficient action is being taken to deal with the problem.
"I told [the referee] that he should stop the game," Ancelotti said. "He said the [league's anti-racism] protocol says that we have to inform [the fans] first, and if they continue, the game stops.
"[Vinicius] is very sad. It's sadness, not anger. The reaction [which saw Vinicius sent off] is quite normal. There are no buts. A stadium made racist insults. Let's see what happens. I'm curious to see. ... Nothing will happen. Usually, nothing happens.
"We can't accept it, we can't tolerate it," goalkeeper Thibaut Courtois said. "If Vini wants to keep playing, we keep playing, but if Vini said he didn't want to play, I'd go off the pitch with him. We can't tolerate these things."
Valencia captain Jose Gaya said: "We condemn these insults. That's what the TV cameras are there for. I hope that if it's clear who [the fan] was, they aren't allowed back into a stadium."
Later on Sunday, LaLiga president Javier Tebas seemed to take issue with the characterisation by Vinicius and Ancelotti of the handling of racist abuse in Spain's top flight.
"Since those who should have, haven't explained to you what LaLiga is doing and can do in cases of racism, we have tried to explain it to you, but you have not shown up for either of the two agreed dates that you requested," Tebas wrote on Twitter. "Before criticizing and insulting LaLiga, it is necessary that you inform yourself properly."
Vinicius received a message of support from home, with Brazil's President Luiz Inacio Lula da Silva calling on the game's world governing body FIFA to stop racism in football.
"I would like to express my solidarity with our Brazilian player, a poor boy who succeeded in life and is potentially becoming one of the best players in the world, certainly the best at Real Madrid. And he is attacked in every stadium he plays in," he told a news conference.
"I think it is important that FIFA, the Spanish league and leagues in other countries take real action, because we cannot allow fascism and racism to dominate football stadiums."
There was also a message of support from FIFA President Gianni Infantino. "Full solidarity to Vinicius," Infantino said, adding that FIFA's three-step process is not easy but needs to be implemented as a means to prevent situations in which players are racially abused.
Gustavo Hofman contributed to this report.