The Blues suffered their worst campaign in the Roman Abramovich era last term after finishing without a trophy in tenth place, which was their lowest position for 20 years.
Speaking about the campaign to Chelsea Magazine, Costa said: "Obviously it motivates me a lot, but I can only talk for myself.
"Everyone has to be their own critic. For me it didn't go well, we didn't honour this great club as we should.
"So we knew that this season, we had to start strong. We had to have this team spirit, this motivation to start well, not just from the first game but from the beginning of pre-season right through to the last game of the season, in order to honour the club."