Though the second automatic promotion place remains a mathematic possibility, West Ham's mental preparations for the play-offs will begin after battling Bristol City held Sam Allardyce's side to a draw that went some way to securing their own Championship status.
"We didn't find the quality of finish," said Allardyce. "We always looked like the dominant force so to finish 1-1 was very disappointing. Maybe the nerve ends are jangling because it is so important to us."
West Ham pressured City from the off, but it was not until the 25th minute when a clear chance was created for James Tomkins' goal, the centre-half scoring with a far-post header from Mark Noble's free-kick.
The home side's equaliser, however, was almost instantaneous. Cole Skuse shot on the half volley from 25 yards and while Robert Green dived well and early, he somehow let the shot fly straight through his hands and into the net.
In the second-half both Henri Lansbury and substitute John Carew went close but the reality was West Ham never truly looked like scoring, especially with City's attempts to contain.
Bristol City (4-5-1):Gerken; Foster, Amougou, Fontaine, McGivern; Bolasie (Woolford, 69), Skuse, Cissé (Adomah, 69), Pearson, Wood; Stead (Carey, 88). Substitutes not used James, Kilkenny.
West Ham United (4-5-1): Green; Demel (Faubert, 74), Tomkins, Reid, Collins (Carew, 63); Lansbury, Noble, Nolan, Taylor, Vaz Te; Maynard (Collison, 74). Substitutes not used Henderson, Diop.
Referee C Pawson (South Yorkshire).