Simeone blamed a lack of balance for his team's defeat, which saw them drift seven points behind league leaders Real Madrid, just a week after they thumped their arch rivals 4-0 to reignite their bid for back-to-back titles.
Atletico started in a 4-3-3 formation with Mario Mandzukic, Antoine Griezmann and Fernando Torres starting up front together for the first time.
With Tiago, Gabi and Saul in midfield, Atletico struggled to keep possession and Simeone pushed Torres onto the left wing in a 4-4-2 early in the first half.
Tiago was withdrawn just after the half-hour mark after complaining about tight calves with Mario Suarez replacing him, while Torres was sacrificed at the break for Cani, as Simeone attempted to regain control of the match.
But Celta scored twice in the second half to win.
"I chose the wrong side in the first half," Simeone said at his post-match media conference.
"I wasted 45 minutes. I made a mistake.
"The fault isn't Fernando's, who had to come off, but because we couldn't balance the side.
"We started the second half better. Then there's the penalty incident and the second goal. Celta played really well."
Simeone explained Tiago was taken off as a precaution but that he had already started to tweak his team tactically: "He [Tiago] was feeling his calves a bit. He asked to come off and Mario went on, but we'd already changed before that, with Torres moving more out left."
Celta opened the scoring in the 59th minute when Nolito converted a penalty after he was tripped by Suarez, while Fabian Orellana doubled the home side's advantage with 19 minutes remaining.
Simeone denied Sunday's result was a fatal blow for his team's title hopes but conceded he will be wary of starting Torres, Mandzukic and Griezmann together again.
"We'll see. I don't know," he said.
"Today it would be hasty to say I would, beyond the fact it didn't go well."
