Spain forward Nico Williams said he was targeted by "monkey" shouts while he took a corner kick in the first half at Metropolitano Stadium.
When he later scored Athletic's goal, he appeared to respond to the insults by tapping his forearm in reference to his skin colour.
"I heard the monkey sounds, but it is always the same two or three people, he said.
"We have to keep working on this. I hope one day it will stop," the 21-year-old said.
His older brother and teammate Inaki Willliams broadened his criticism to include the fans who jeered after Nico responded to the incident.
"They jeered him every time he touched the ball," Inaki Williams said.
"I can't understand that. They should jeer the aggressors, not the victim."
Atletico captain Koke condemned the incident, saying he and his teammates "were with Nico".
"I send Nico all my support, along with my teammates and the club. There is no place in soccer for what happened," Koke said.
"These people must be identified and not allowed in the stadium."
The Spanish league has been unable to stop repeated verbal racist attacks against players, with Real Madrid forward Vinicius Junior among those consistently targeted.
The first trial against a fan accused of racial abuse in Spanish professional soccer - following insults aimed at Inaki Williams from an Espanyol supporter in 2020 - is still waiting to be scheduled.
Atletico, in fourth place, opened a six-point gap over Saturday's opponents in fifth with five games remaining. The top four finishers in La Liga will qualify for next season's the Champions League.
Midfielder Rodrigo de Paul put Atletico ahead in the 15th minute when his long shot took a deflection to beat Spain goalkeeper Unai Simon.
Nico Williams levelled just before halftime, capitalising after a poor pass from Atletico star Antoine Griezmann.
Angel Correa restored the home side's lead in the 52nd minute and the game was put beyond doubt with 10 minutes remaining when Samuel Lino's shot hit the post and bounced in off the keeper.
Girona moved into second place by winning at Las Palmas 2-0 in the Canary Islands, although Barcelona will overtake them if they beat Valencia on Monday.
Defender David Lopez scored in the 26th minute and Artem Dovbyk converted a penalty in the 57th to take his league-leading tally to 19 goals.
Girona goalkeeper Paulo Gazzaniga saved a penalty by Sandro Ramirez with the score still 0-0.
Mason Greenwood scored twice and set up a third to lead Getafe to a 3-1 win at last-placed Almeria.
Giuliano Simeone, the son of Atletico coach Diego Simeone, scored his first goal since joining Alaves to help them to a 3-0 win over Celta Vigo.
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