Fernando Baiano, with his 12th goal of the season, got one back for Celta on 62 minutes.
Athletic continued their fight to preserve their historic status as one of only three teams to be ever-present in the Spanish first division — along with Barcelona and Real Madrid — by drawing 1-1 with Deportivo La Coruna.
"We lost a good chance to put some space between us and the relegation zone," Athletic coach Mane Esnal reflected.
Athletic are just one place above the relegation zone but have a four-point advantage over their fellow Basques Real Sociedad.
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