Miroslav Djukic's side crashed to a 3-1 defeat to Espanyol at Cornella-El Prat at the weekend, having edged a 1-0 win over Malaga in their first Liga game.
However, Costa is determined to bounce back from that disappointing performance but says his team-mates must up their game to beat the Blaugrana.
"We have to improve, work harder and raise our game against Barca. We will have to be perfect to beat them," Costa told AS.
"We really paid attention to [coach Miroslav] Djukic after the match.
"And it was the right time to do so. We feel ashamed of the game we played at Cornella-El Prat."