In a game dominated by Celta, Diego Simeone's men struggled to hit the heights of last weekend's 4-0 demolition of Real Madrid and will be particularly unhappy with the award of the penalty converted by Nolito.
Augusto Fernandez clearly handled the ball in the build-up, but the referee played on and Nolito was brought down before getting up to convert the spot-kick himself.
Eduardo Berizzo's side controlled the first half and were well worth a lead that should have been doubled by Joaquin Larrivey.
Either side of that chance, Saul Niguez and Antoine Griezmann forced fine saves from Sergio Alvarez as the game sprung to life, but Atletico conceded again after 71 minutes as the impressive Orellana lashed home to keep the champions seven points behind leaders Real after a first league defeat at Celta since 2005.
Fernandez handled the ball in the centre of the pitch, but nothing was given and in the same move, Nolito was brought down in the area by Mario Suarez.
The champions were almost level a minute later as Niguez's rasping drive was parried by Alvarez, who then made a miraculous save to tip away Griezmann's rebound, although the Frenchman was given offside.
It sparked the game into life and Celta should have been out of sight a minute later as Nolito squared to Larrivey, but, with the goal at his mercy, he somehow missed the target.
Back at the other end, Griezmann went agonisingly close to a leveller, but his well-struck shot was blocked by Alvarez, who managed to gather just before the ball crossed the line.
But Celta rounded off a great team performance with 19 minutes remaining when Krohn-Dehli found Orellana in space and he lashed home from inside the area to give Miguel Angel Moya no chance.
