Both teams lacked creativity and any real threat throughout the contest and the main talking point came when Baggies goalkeeper Ben Foster wiped out Javier Hernandez on the edge of the box in the second half.
The former England international lunged into a challenge with his studs showing and was lucky more contact was not made against his Mexican opponent, who was down on the floor for a few minutes.
A yellow card was shown to Foster and that was the main talking point, of the second half at least, as neither side came close to troubling either goal, highlighting the poor quality on show.
West Ham's best chance came in the opening 45 minutes when midfielder Pedro Obiang saw the keeper off his line and crashed an effort from 45-yards out against the bar.
The home side missed out on a good chance in the first half when James Morrison, free in the box, failed to make significant contact with his head and the ball skimmed off his forehead.
One worry for the Hammers will be a potential injury to James Collins after he was forced off the field of play in the second half when going down on the halfway line under no pressure.