Simeone's side endured a frustrating time in front of goal at the Estadio Wanda Metropolitano on Saturday as they were held to a goalless draw.
Costa, 30, was booked after the final whistle for his part in an ugly fracas with the Celta Vigo players.
When asked a question about Costa's attitude for his role in the aftermath, Simeone claimed he "didn't see" the incident.
However, the Argentinian has backed Costa to come good even though the ex-Chelsea forward has not found the net in a competitive match since he scored against Alaves in March.
"The numbers are what you say, it's the reality, but I trust Costa," Simeone said.
"I know he'll be fit again and it's a challenge for him. The championship is long and the team needs him."
Simeone called on Costa and the club's other strikers to become more ruthless after Atletico's return of just seven goals in five LaLiga matches in this season so far.
"I think we started the pre-season at a great level, especially for strikers," added Simeone.
"The team looked good and it gives me the feeling that it is normal, when the season starts there are spikes and immediately the goals appear and in others they disappear.
"Hopefully we can get the focus to play back because the situations are there.
"If we do not, we must try to increase the offensive intensity because the goal comes from the rage of wanting to make a goal."