Costa had a goal disallowed and missed a penalty.
Nevertheless, Simeone has made clear he will continue to trust the player as long as he keeps working hard.
"When someone works as hard as Diego Costa, I will continue to trust him," Simeone explained in his post-match interview.
"Diego is currently at his best physically; he is training well but can't find the goal.
"You're either with Costa or without Costa. I'd give my life for him."
"I saw it as a very good game, Sevilla always compete well," Simeone added.
"They have a lot of players, a deep squad and they are able to make changes.
"Fernando [Reges] wasn't playing today but they could call on [Ever] Banega. They have many options and if they can maintain that, they will always compete."