Diego Simeone's side had been hoping to prove its struggles in a UEFA Champions League stalemate against Porto in midweek were not indicative of wider problems, but it disappointed the home crowd again.
Atleti had looked promising at the start, though Athletic soon grew into the game and was defensively able to frustrate the hosts.
Inaki Williams was unable to make the most of a rare moment of defensive frailty from Los Colchoneros, though they were never made to rue his miss as Atletico failed to break the deadlock, the post denying Marcos Llorente late on before Joao Felix's red card encapsulated the home side's frustration.
Atletico enjoyed some pressure during the early exchanges, with Antoine Griezmann shooting wide from close range and Stefan Savic heading into the arms of Unai Simon from a similar distance.
But those half-chances were hardly precursors to a sustained onslaught, with Atletico not worrying Athletic again before the break.
They came out after the interval with renewed purpose, as Angel Correa headed just wide from Renan Lodi's cross.
But Athletic crafted the best chance of the game two minutes later, Williams poking the ball through Jose Gimenez's legs before charging through on goal, only to let Atletico off the hook by not even hitting the target when one-on-one with Jan Oblak.
Simeone turned to Luis Suarez – seemingly dropped after an ineffective showing against Porto – as he made four substitutions in five minutes before the hour, though the Uruguayan's lack of pace was glaring when unable to run through on goal when released by fellow substitute Yannick Carrasco.
Llorente attempted to take matters into his own hands but saw his long-range effort crash off the post, before Atletico's chances took a final blow when Joao Felix, another substitute, was booked twice in quick succession, the second for dissent, and he left the pitch in a furious mood.
Asier Villalibre then squandered a glorious chance to win it in stoppage-time, slicing over with only Oblak in his path.