Diego Simeone's men currently sit three points adrift of leaders Real Madrid in the Spanish top flight, having kept pace with their local rivals and Barcelona for the duration of the season so far.
Atleti take on Real in the Madrid derby on Sunday, but suffered a setback last weekend as they fell to a 3-0 defeat at Osasuna.
However, Costa believes the 2013 Copa del Rey champions have never been realistic title prospects.
"I'm really excited about playing in the derby," he is quoted as saying by Marca. "As soon as the Osasuna game ended, I was already thinking about the next match. I'd been thinking about it for a while. We're going to go into that game as if it were our last.
"We know the derby is very important, but we can't lose hope over one game.
"If we lose against Real Madrid, it is going to be much tougher (to win the title), but to be honest, we've never really been title contenders. We've been fighting against everyone.
"We're doing well and we know that we're back in the fight again if we win."
Costa and Real defender Sergio Ramos clashed in last season's December derby at the Bernabeu, with the Spain defender spitting at the striker after they had earlier butted heads.
However, having made headlines for the right reasons after sealing a 1-0 victory for Atleti in their neighbours' stadium earlier this season, Costa says he will stop at nothing to ensure victory once again.
"I'm no saint in the matches, but against Madrid you saw that I wasn't looking for a fight at any time," he added. "I fought and tussled with Ramos.
"If I have to hit him, I'll hit him. If he has to hit me, he'll hit me, but always in a loyal way, always within the bounds of the game."
