The Reds came close on a couple of occasions, with Celin Bizet and Gabby George both hitting the woodwork in the first half.
West Ham had a few chances of their own in the second half, which Phallon Tullis-Joyce was across with relative ease.
United, meanwhile, pushed for a winner with Grace Clinton coming close with a long-range effort, but ultimately we couldn't find a way through the Hammers' defence.
FIRST HALF
West Ham started the game strongly with an early chance from a set piece, but Eva Nystrom headed wide Viviane Asseyi's delivery.