Atleti lead the Spanish top flight by three points from Real Madrid and Barcelona ahead of Friday's clash with Elche.
With Barca playing on Sunday and Real not in league action this weekend, Atletico could move six points clear and Costa claims Diego Simeone's side are capable of becoming champions.
With a UEFA Champions League semi-final against Chelsea to consider, the Spain international issued a rallying cry ahead of a decisive month.
"Now is a very crucial month. We know what we have to do," he told AS.
"The team has the mentality, strength and conviction. It's very important and we will give everything.
"At home, with the supporters, we are very strong."
Costa had been a doubt for the game after suffering a gashed knee following a collision with the post in Sunday's win over Getafe.
However, Costa says he is available for selection as he looks to add to his 26 league goals this term.
"I'm fine. The truth is it was a scare and thank God nothing happened," he added.
"I'm eager to play."
