Costa was forced off on a stretcher in the closing stages of the match after he collided with a goalpost when scoring Atletico's second goal.
The Spain international's left leg crashed into the frame of the goal after he had tapped in Adrian Lopez's cross, with the incident leaving a large gash towards the top of his shin.
The 25-year-old's team-mates were visibly distressed as they motioned to the bench for the striker to be replaced, but Simeone confirmed that the forward has not done any serious damage.
Atletico revealed on their official Twitter account: "Luckily Diego Costa has only one injury (the wound) after hitting the post."
And Simeone added: "Diego is well and he is fine. One more cut won't do anything to this tiger."
Centre-back Diego Godin notched Atletico's opener in what turned out to be a routine victory, which sees them go three points ahead of Real Madrid once again at the top of La Liga.
Simeone was impressed with his side's professional display at the Coliseum Alfonso Perez, acknowledging that the league leaders have everything in their own hands with five games left.
He added: "I always said that (winning the title) depended on us and I still maintain that. This depends on the ambition, enthusiasm, effort, work-rate and especially the humility of the team.
"We did a great job (at Getafe). It was a tough game which took effort and ambition on the part of the players to acquire a result which is very important.
"This leaves us where we wanted to be with five games to go. We have five finals now and we have to play them as such.
"Now we focus on the match against Elche as that is the next game. There is no other thought than to prepare for that and rest."
