Even with the King's Cup semi-final first leg against Barcelona coming up on Wednesday, Diego Simeone fielded a full-strength team against Alaves but he watched his side get outplayed by the Basques, who are without a win in the league in 2017.
Alaves defender Victor Laguardia struck the underside of the bar with a hooked volley in a strong first-half display from the home side, Brazilian forward Deyverson somehow heading over the bar on the rebound from close range.
Mauricio Pellegrino's side, who like Atletico also booked their place in the Cup semi-finals last week, continued to dominate proceedings after the break and midfielders Victor Camarasa and Edgar Mendez both spurned chances while Atletico loanee Theo Hernandez was denied a goal against his parent club by goalkeeper Miguel Angel Moya.
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Atletico's Argentine midfielder Nicolas Gaitan had a glorious chance to snatch what would have been a scarcely deserved win for the visitors when he found himself through on goal but he failed to successfully dribble around custodian Fernando Pacheco.
Simeone's side have won just one of their last four away games in the league in what has been their worst campaign since the Argentine coach took charge in December 2011.
Atletico are fourth on 36 points and could drop to fifth if Real Sociedad win at leaders Real Madrid on Sunday; Alaves are 12th on 24. Champions Barcelona, in third, visit Real Betis on Sunday, while second-placed Sevilla travel to Espanyol.
"We leave here with a point which is more than we deserved given how we played. It was a bad game from our point of view and Alaves were better than us in every aspect, especially in intensity," Simeone told reporters.
"It was not a good performance and we have to try and improve so we can do better in our next game (against Barcelona)."
Earlier on Saturday, Villarreal picked up their first win in seven games in all competitions by beating basement club Granada 2-0 at home with goals from Bruno Soriano and Alvaro Gonzalez either side of halftime to tighten their grip on sixth place.
Granada returned to the bottom of the league following Osasuna's 1-1 draw at home to Malaga on Friday.
(Editing by Clare Fallon)
