Costa had not scored in the league since February but ended his longest ever drought in the top flight with a header from Antoine Griezmann's corner.
That had Atletico on track to leapfrog Barcelona into top spot in the La Liga table, but Barca hit back to deny Simeone his first league win in this fixture during his seven years as Atletico coach.
Lionel Messi teed up late substitute Ousmane Dembele, who cut inside to steer a low shot past Jan Oblak and desperate defender Lucas Hernandez on the line to snatch a point.
"He retired with a little discomfort in his foot and asked for the change," Simeone said to Movistar .
But Simeone will want Costa to shake off the injury, with his first goal in 10 La Liga appearances against Barcelona potentially a turning point in his season.
"We hope so," Simeone said of Costa's previously poor form being boosted by his header.
"He's an animal, and every time he's on the field the team has a chance to win."
Atletico stifled Barcelona for much of the top-of-the-table contest, with only two shots on target recorded by either side.
"The style was very similar because we both played something similar," Simeone said.
"I liked everything, we had a commitment, we were close to winning."
Atletico beat Monaco 2-1 in their first Champions League meeting of the year, Costa scoring to pull his side level before Jose Gimenez hit the winner.
And the French side had remained winless since that match until Saturday, when Thierry Henry picked up his first victory in change of the club with a 1-0 result against Caen .
Monaco have already been knocked out of Champions League contention, while Atletico sit level on points with Dortmund at the top of Group A.