Despite the Blues having held a lead on two occasions, a error from goalkeeper Edouard Mendy gifted West Ham a penalty, while the Senegalese stopper was unable to react quick enough to prevent Arthur Masuaku's deflected cross from going inside the near post.
While the winning effort was a touch of good fortune over a glaring mistake from Mendy, Chelsea made a number of errors as a team, something which Tuchel was quick to allude to after the final whistle.
Speaking to BT Sport, Tuchel said: "I don't think we did a bad match, it was OK, we can win with this performance.
"It is tough to play here, we did too many individual mistakes, we did already against Manchester United and Watford and got punished - if you want a result at this level you have to minimise mistakes. We talked about it before, it's obviously not helped."
Commenting on the first-half penalty, the German added: "Everybody is involved, the pass is not the best decision, the orientation is not the best, we can save it but the decision-making is also not the best from Edu in this moment.
Chelsea will drop to third position in the Premier League standings if Manchester City and Liverpool are able to overcome Watford and Wolverhampton Wanderers respectively.