• BBC Sport understands two fans have been identified for racially abusing Vinicius and are expected to be given permanent stadium bans by Valencia.
• La Liga said in a statement that it will investigate and take "appropriate legal action" if a hate crime is identified, calling on people to submit any relevant footage.
Real Madrid forward Vinicius Junior said "La Liga belongs to racists" after being subjected to racist chants at Valencia.
The 22-year-old Brazil international was dismissed for violent conduct in the 97th minute of the 1-0 La Liga defeat after an altercation with Hugo Duro.
Earlier in the game, an incensed Vinicius attempted to bring Valencia fans to the referee's attention.
"The championship that once belonged to Ronaldinho, Ronaldo, Cristiano and Messi today belongs to racists," Vinicius wrote on Instagram.
"It wasn't the first time, nor the second, nor the third. Racism is normal in La Liga. The competition thinks it's normal, the federation does too and the opponents encourage it.
"A beautiful nation, which welcomed me and which I love, but which 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, for everything that happens each week, I have no defence. I agree. But I am strong and I will go to the end against racists. Even if far from here."
BBC Sport understands two fans have been identified for racially abusing Vinicius and are expected to be given permanent stadium bans by Valencia.
La Liga said in a statement that it will investigate and take "appropriate legal action" if a hate crime is identified, calling on people to submit any relevant footage.
Writing on Twitter, La Liga president Javier Tebas said Vinicius twice did not turn up for a meeting to discuss what it "can do in cases of racism".
"Before you criticise and slander La Liga you need to inform yourself properly," Tebas said.
Vinicius criticised the post for targeting him instead of the "racists", saying he wants La Liga to take "actions and punishments".
'An entire stadium chanting racist slurs'
Vinicius has been the subject of racist abuse several times this season.
The game was paused in the 70th minute as Vinicius tried to point out fans in the crowd whom he believed were abusing him.
He was ushered away by team-mates and Valencia players, before being spoken to by referee Ricardo de Burgos and Real Madrid manager Carlo Ancelotti.
Vinicius was later sent off for the first time in La Liga for his involvement in a mass altercation between the two sets of players.
Ancelotti said: "What we saw today is unacceptable - an entire stadium chanting racist slurs.
"I don't want to talk about football today. There is no meaning in talking about football today. I told the referee he should have stopped the match.
"La Liga has a problem. For me Vinicius is the most important player in the world. These episodes of racism have to stop the match.
"It's the entire stadium that is insulting a player with racist chants and the match has to stop. I would say the same if we were winning 3-0. There is no other way."
Ancelotti said Vinicius' reaction was "understandable" in the circumstances.
"I asked him if he wanted to keep playing, and he stayed in the game," Ancelotti said.
"Vinicius is very sad; he is angry. Something like this can't happen in the world we live in."
Valencia said they will investigate and "take the most severe measures".
"Valencia CF wishes to publicly condemn any type of insult, attack or disqualification in football," a club statement read.
"Although this is an isolated episode, insults to any player from the rival team have no place in football and do not fit in with the values and identity of Valencia CF."
La Liga said it had been proactive after previous racist abuse against Vinicius, and had filed nine reports in the past two seasons to legal authorities in Spain.
Fifa president Gianni Infantino said he had "full solidarity" with Vinicius and highlighted the world governing body's protocols for events like those at Valencia.
"Firstly, you stop the match, you announce it. Secondly, the players leave the pitch and the speaker announces that if the attacks continue, the match will be suspended," he said.
"The match restarts, and then, thirdly, if the attacks continue, the match will stop and the three points will go to the opponent. These are the rules that should be implemented in all countries and in all leagues.
"Clearly, this is easier said than done, but we need to do it and we need to support it through education."
Former England and Manchester United defender Rio Ferdinand wrote on Instagram: "Bro you need protecting.... who is protecting Vinicius Junior in Spain??
"How many times do we need to see this young man subjected to this? I see pain, I see disgust, I see him needing help... and the authorities don't help him.
"People need to stand together and demand more from the authorities that run our game.
"No-one deserves this, yet you are allowing it. There needs to be a unified approach to this otherwise it will be swept under the carpet AGAIN."
Real goalkeeper Thibaut Courtois said he heard some "monkey noises" after 20 minutes.
"If Vini wants to keep playing, we keep playing, but if Vini says he's not playing any more, I'm leaving the pitch with him, because we cannot tolerate these things," Courtois told Movistar.
Brazilian football federation (CBF) president Ednaldo Rodrigues said: "How long are we going to experience, in the middle of the 21st Century, episodes like the one we just witnessed, once again, in La Liga?
"How long will humanity remain just a spectator and an accomplice in cruel acts of racism?"
Juan Castro, a journalist for Marca who was at the game, told BBC World Service: "Valencia fans abused Vinicius and called him a monkey.
"We have a problem here in Spanish football and we have to solve it. It's the 10th time that this has happened to Vinicius.
"Maybe the solution is to suspend the match. Maybe the solution is that Vinicius decides not to be on the field any more. Maybe that will be the solution to make people aware that they cannot behave like this in a football stadium."