Villarreal midfielder Manu Trigueros intercepted a weak back pass from Tiago Mendes before firing the ball into the bottom corner in the 28th minute.
Jonathan dos Santos then nipped in to grab the second goal in the 38th minute after Oblak spilled a shot from Alexandre Pato.
Roberto Soriano capped a first win in four league games for Villarreal by finishing off a one-two with Alfred N'Diaye in injury time at the end of the match.
"I leave with the sensation that the team is fighting, working hard and trying to do everything to win but results aren't going our way," said Simeone.
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"We have to keep working because that's the only way we'll improve."
Oblak was taken to hospital for tests on a shoulder problem he sustained when trying to prevent Dos Santos reaching the loose ball.
Tiago had also been taken off immediately after his error, complaining of discomfort in his knee.
"Oblak's injury is worse, we hope it's not too serious," added Simeone.
"Tiago's knee was bothering him and he realised the best thing to do was to ask to come off."
Villarreal leapfrogged Atletico into fourth place with 26 points from 15 games. Simeone's side dropped to sixth on 25 and may now have to target a top-four finish rather than a title push.
"The result does not reflect the story of the game but when you commit errors like the ones we made you end up paying for them," said Atletico captain Gabi after the visitors were beaten for the fourth time in seven league matches.
"We need to improve so we can get back towards the top of the table."
(Reporting by Richard Martin; Editing by Tony Jimenez and Ken Ferris)
