Despite his side picking up a surprise result at the home of the defending champions, Moyes insists that he will not be happy until United reach 40 points for the season - six more than their current total of 34.
"We were incredibly committed. Thankfully we stuck at it and got something out of it," he told Sky Sports News. "Chelsea were really good in the first half but we kept it to one. The goal we lose is dire - I could accept conceding from some of their great play but the goal was so poor.
"Maybe on another day we get a penalty late on as well. I've always said we need 40 points; we might not need them but we won't be happy until we get there."
West Ham have six more games left to play, beginning with a home match against Stoke City on April 16.