And Atletico can take little comfort from their run-in after this weekend, which will see them finish at home to Sevilla and away at Real Sociedad after a more winnable game away at Elche.
“I’m concerned as I’ve always said,” Simeone said after the loss to Athletic.
“You have to know how to handle difficult moments, which have been rare in these last few years.
“The responsibility is mine and it depends on me whether the players stay calm or not.”
If Betis had been more consistent in recent weeks they might already have Champions League qualification in their own hands but two draws against Real Sociedad and Getafe, either side of a loss at home to Elche, have allowed Atletico to hold their ground.
Manuel Pellegrini’s side may have had their focus diverted by the final of the Copa del Rey, which they won last month against Valencia, but the top four is still within reach, despite difficult remaining games against Barca, Valencia, Granada and then Real Madrid.
Sevilla, in third, are still not home and dry but their six-point lead over their city rivals should be enough, even if they have a tough game on Sunday away at Villarreal.
Unai Emery’s side might still be licking their wounds after their Champions League exit at the hands of Liverpool on Tuesday.
At the other end of the table, Mallorca host Granada on Saturday in what looks a crucial game in the battle to avoid relegation, with Mallorca and Cadiz just one point ahead of Granada as all three teams fight to escape the drop.
Fixtures (GMT)
ترتيب الدوري السعودي للمحترفين
Levante vs. Real Sociedad (1900)
Saturday
Mallorca vs. Granada (1200), Athletic Bilbao vs. Valencia (1415), Celta Vigo vs. Alaves (1630), Cadiz vs. Elche (1630), Real Betis vs. Barcelona (1900)
Sunday
Getafe vs. Rayo Vallecano (1200), Villarreal vs. Sevilla (1415), Espanyol vs. Osasuna (1630), Atletico Madrid vs. Real Madrid (1900)