The Blues suffered a rare wobble on Saturday to keep the chasing pack interested in a battle for the top-flight crown.
A 2-1 defeat at home to Crystal Palace has seen their advantage over second-placed Tottenham cut to seven points, with a visit from Pep Guardiola’s City side in midweek representing the first of several big games to come.
"After a loss at home and with a rival closing the gap the importance of the game only grows," Costa is quoted as saying by ESPN Brasil.
“We know this game against Manchester City will be a six-point affair since if we win the game they will [practically] be out of the title race while we keep the advantage.
"It also depends on the match between Tottenham and Swansea. In any case, we will do our best.
“We hope that the next game the ball will go in, and that we do a better job at handling these counter-attacking plays so we do not suffer from early goals again, and thus avoid what happened [against Palace]."
City are 11 points behind Chelsea at present, with just nine games of the campaign remaining.
For now, though, Costa and his team-mates are focused on righting the wrongs of a derby defeat to Palace.
He added: “We started off well, we scored and in two counter-attacking plays they managed to get two goals.
“They have two good players up front and knew how to utilise it the best way they could. Afterwards they got behind the ball, we created opportunities and the ball did not go in.
"Obviously, as time passes by in the second half you do not go forward with a clear head. You go on with effort and will, but things do not solve themselves this way. At least we tried, and we did everything we could to get a draw.
"But now it is not the time to let ourselves down. We should keep our heads up and think ahead for the next game since it will be very important."
The Blues will be hoping to see Costa get back on the scoresheet in that contest, with their 18-goal top marksman having gone three domestic games without finding the target.