Valencia walked off the pitch during Sunday's 2-1 La Liga defeat at Cadiz after an alleged racist comment, before later returning to complete the match.
Mouctar Diakhaby reacted furiously after a first-half clash with Cadiz's Juan Cala and spoke with the referee.
Valencia's players left the pitch in protest and the club said Diakhaby, 24, "received a racial insult".
He later asked his team-mates to return and they resumed the game but without Diakhaby, who was substituted.
Valencia defender Jose Gaya said after the game that the team either had to resume playing or risk a points deduction.
"Diakhaby told us he heard a racist insult so we all went off the pitch," Gaya told Spanish network Movistar.
"We were told that we had to play because if we didn't, they would take the three points off us and maybe we'd be docked more points.
"Diakhaby asked us to play on. We wouldn't have done so if he hadn't done so. He said he wasn't in the right state of mind to keep playing. He is devastated."
The game was 1-1 at the time, with Kevin Gameiro having equalised after Spanish defender Cala opened the scoring for Cadiz.
Cala, 31, was also substituted at half-time, before Marcos Mauro's 88th-minute goal gave Cadiz a 2-1 victory.
"We offer our complete backing to Mouctar Diakhaby," Valencia said of the decision to return to the pitch.
"The team have held a meeting and decided to continue the game, in order to fight for the honour of the club, but denounce racism of any kind."
Gaya said he had heard the comment Cala made to Diakhaby.
He added: "It was a very ugly insult which I won't repeat. We haven't been able to speak with Cala because he was the last player to leave the pitch. I'm certain that he said something. It was a very strange game."
Cadiz said they were "against any manifestation of racism or xenophobia", regardless of who the perpetrator was and that "they work hard to help eradicate" discrimination.
"Anyone guilty of such an offence, whether or not they belong to our team, must be punished," Cadiz said in a statement.
"We have complete confidence in the integrity of our squad members, who are staunch supporters of the fight against racism."
While Cala was not mentioned by name in the club statement, Cadiz boss Alvaro Cervera said the defender "insists he did not insult" Diakhaby.
"Cala says that at no point did he insult the opposition player," Cervera told the club website.
"It's the fist time something like this has happened to us and we did not know how to react. There was a lot of confusion.
"We're a faithful, honest team and we don't do this kind of stuff. That's what I can say."
On Monday, the Spanish league said it "condemns racism in all shapes and forms" and added that it had been an active party in tackling hate crimes in the country.
"We take any allegation of racism seriously and will work with the clubs and refereeing establishment to do whatever is necessary to protect the values of equality and respect that prevail in our Spanish professional football competition," the statement from La Liga continued.