Williams said he was the victim of racist abuse during Bilbao's 1-1 draw at the RCDE Stadium on Saturday, with La Liga pledging to ensure those responsible are also handed bans from football stadiums.
"La Liga wishes to express its rejection and deepest concern regarding the events that occurred yesterday," a statement read.
"We are aware that measures taken in recent years have seen improvements but while they have seen a decrease in violent insults and attitudes both inside and outside the football stadiums, they remain insufficient, according to the evidence from yesterday."
The statement added: "La Liga has already initiated a procedure to identify the fans that made insults against Inaki Williams in order to initiate criminal proceedings for a Hate Crime."
La Liga said it would also carry out a review of ticket sales and "report any type of violent, racist and/or xenophobic behaviour to the Anti-Violence Commission so that the fans involved can be sanctioned with bans from access to football stadiums."
The RFEF also condemned the racist chants directed at Williams.
"The RFEF considers the racist attitudes or chants made yesterday at the stadium of RCD Espanyol by a very small number of people in the section of RCD Espanyol are, regardless of the number of people involved, extremely serious".
Referee Jose Sanchez made no mention of racism in his official report.
The game also continued, unlike in December, when a Spanish second division fixture between Rayo Vallecano and Albacete was suspended with the agreement of the two clubs and La Liga.
Some Rayo supporters had chanted "Zozulya is a Nazi" in the first half against Albacete's Ukrainian striker Roman Zozulya, who had previously played for Rayo.
"During the fixture none of the referees or assistants noticed any problems in this regard," the RFEF statement added.
"In order to adopt any measure, it must first be known that what happened and this was not the case."
Williams told Bilbao's official club website after the game: "I'm a little sad because of the draw but especially because I have suffered racist insults. It's something that no black player or player of any race wants to hear. It's something totally out of place."
Inaki wrote later on social media: "It is very sad that today we continue to experience racism in football. We have to end it. Thank you for your support. #NOalRacismo #SayNoToRacism."
Athletic Bilbao offered their backing for the 25-year-old. "All our support to @Williams45," the club wrote in a message on Twitter. "Before anything, zero tolerance for racism."