Referee Clos Gomez wrote in his match report that he suspended play during the first half when he said he heard "monkey calls" being shouted from one section of El Molinon Stadium directed at Williams.
Gomez explained that play was only suspended for a minute while a warning given by the public announcer. The abusive insults then stopped.
The 22-year-old player was born and raised in Bilbao by a Ghanaian father and Liberian mother, and joined Athletic's youth squad when he was 18, becoming the first black player to score for the 'Basque only' club in 2014.
Since then he has made over 60 appearances for his club and earned his first national team cap for Spain in May.
The issue of racism in Spain's favourite sport was highlighted in 2014 when Barça's Dani Alves paused to pick up a banana thrown at him during a game.