Victor Laguardia scored the only goal four minutes in at Estadio de Mendizorroza to inflict a first defeat of the season on Atleti in all competitions.
😱 UPSET ALERT 🚨 @Alaves stunned @Atleti today, registering a first win after five defeats in the 21/22 #LaLiga campaign as the champion in turn suffered its first defeat!! More here 👉🏻 https://t.co/igjdfscF2L | #AlavesAtleti pic.twitter.com/IRdPphqMGV— beIN SPORTS (@beINSPORTS_AUS) September 25, 2021
Atleti had just one shot on target – substitute Angel Correa forcing Fernando Pacheco into a fine save – as Simeone's side missed out on the chance to overtake leader Real Madrid, a disappointment amplified as Los Blancos endured a goalless stalemate against Villarreal later in the day.
The Spanish champion has now failed to find the net in three of its past four matches, during which time it has won only once in all competitions.
Despite playing a full part against Alaves, which was without a point this term, Luis Suarez and recent signing Antoine Griezmann failed to complete a single pass between each other.
Griezmann has yet to register a shot on target in his past seven LaLiga outings for Atleti and Barcelona combined, his longest such run in Spain's top flight.
Rather than criticise the likes of Suarez, Griezmann and Correa, Atleti boss Simeone instead insisted it was down to him to find a way to break down a solid Alaves team.
"The responsibility is mine for not having found options to overcome their defence," he said.
"When opposition teams defend well, it is difficult to find those solutions.
"It's also difficult when a team like Alaves close you down. We didn't have the speed or ability to hurt them. They deserved the win because they scored and knew how to defend."
Laguardia's early goal came from a set-piece situation, the centre-back getting away from Stefan Savic and heading in Ruben Duarte's corner.
Half of the previous 10 goals conceded by Atletico in the league have now come via headers, excluding own goals, and Simeone accepted his side must improve in that area.
"I don't think the defence is to blame for the defeat because the goal came from a set-piece," he said.
"But if there's a weakness at the back, or when defending set-pieces, then it is clear we will have to study that, work on it and try to correct it.
"We have to keep improving. We had several phases of patient play today and I believe in these players."
Atleti's fixtures do not get any easier as it travels to AC Milan in the UEFA Champions League on Wednesday (AEST), then hosts Barcelona in the league four days later.
Reflecting on a bad run of form heading into that huge double-header, Simeone added: "We always say there are bad moments during a season and this may be one of them.
"We have a good squad, a balanced squad, and we will analyse what is going wrong and try to find solutions."