Atletico went into the game eight points adrift of pacesetters Barca, meaning anything other than a win would be of little use in the title race.
Their chances took a major blow in the 28th minute when Costa was given his marching orders after appearing to say something to referee Jesus Gil Manzano.
Luis Suarez and Lionel Messi secured the win – and probably La Liga – with goals in the last five minutes, though much of the post-match focus remained on Costa.
"In the last 11 games here [at Camp Nou] we have received seven red cards," Simeone told reporters. "We must be doing something wrong.
"I asked the referee and he told me something that Costa says he didn't say. If he said it [what the referee claims], he is deservedly sent off.
"But other players have said things and he doesn't send them off. We see it and they do not send them off.
"But that does not justify Costa's actions. If the referee interprets that there was insult, he's deservedly sent off, but it's not always the same [outcome for every player]."
Simeone was also eager to move away from the negativity many have attached to the defeat, with some suggesting their season is over, although he believes such opinions show how far the team has come.
"Our season has not ended in any way," he said. "We have to win as many points as possible.
"I value that we won the European Supercup, that we fought for the second place, and it is bad? I love it, I love that it is said to be bad [the season]. Do not forget where we are."
Now 11 points behind the leaders and just two ahead of arch-rivals Real Madrid with seven games remaining in the campaign, Atletico's next test will come on Saturday at home to Celta.
Barca could go 14 points clear with a win over bottom side Huesca, with that clash finishing just minutes before Atletico kick off in the Wanda Metropolitana.