Felix, Atletico's record signing, was shown a yellow card for striking Unai Vencedor in the 78th minute and the Portuguese reacted to the decision by shouting at the referee, who instantly produced a second card and sent him off.
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Felix had only been on the pitch for 18 minutes when he was dismissed, with Spanish media reporting the Portuguese said "Are you crazy?" to match official Jesus Gil Manzano after being penalised for tangling with Vencedor as they challenged for the ball.
Diego Simeone's side are top of the standings with 11 points from five games while Athletic, who are also unbeaten, have nine.
"Joao was running and had no intention of hitting his opponent, I don't know what happened next but people say things in the heat of the moment but they [referees] have to understand that when your adrenaline is running high you sometimes say things you shouldn't," Atletico defender Stefan Savic said.
Atletico were fortunate to not lose the game in added time when visiting striker Asier Villalibre met a through ball from Alex Berenguer inside the area but the forward somehow spurned the glorious chance and missed the target.
Atletico created few opportunities in another uninspiring home performance following Wednesday's 0-0 draw with Porto in the Champions League, with their best moment coming when Marcos Llorente struck the far post with a shot from outside the box.
Antoine Griezmann made his first league start at the Wanda Metropolitano since returning to Atletico on loan from Barcelona but the Frenchman had another poor display and was hauled off in the 55th minute as part of a triple change from Simeone.
"It can happen to any player," Simeone said on the red card. "The ref understood that he had to send him off. If someone else did it, maybe he wouldn't think the same."
When asked about his conversation with the referee afterwards, he replied: "I asked him to be calm, he said to me that I couldn't ask him to be calm, that he already was.
"He's a great referee, he's had very good performances. Depending on the day, sensitivity can cause different feelings."