A hard-fought encounter saw Matt Beard’s side create more of the genuine chances but neither team could produce a decisive moment.
It means they remain as they were in the Barclays Women’s Super League, with West Ham one point above the eighth-placed Reds.
The hosts forced the first chance at Chigwell Construction Stadium when, four minutes in, Lisa Evans worked space with a dribble down the right-hand side.
Her delivery into the Liverpool area was dangerous and Emma Koivisto did brilliantly to head the ball over the crossbar before Dagny Brynjarsdottir could connect from close range.
Koivisto was next in action at the other end as the Reds threatened an opening goal on three occasions in quick succession.
First, the wing-back’s deep cross drifted menacingly in the direction of the top left corner and had to be clawed away by retreating Hammers goalkeeper Mackenzie Arnold.
Missy Bo Kearns’ resulting corner swerved towards goal in similar fashion – and was repelled by Arnold right under the bar – before a header on the follow-up from Leighanne Robe, making her 100th Liverpool appearance, was cleared.
Next, Megan Campbell hoisted a pass that caused concern inside the West Ham box and ran to Yana Daniels, whose close-range strike was wide.
Much of the remainder of the half was evenly matched and short on scoring opportunities of note, though the visitors had a sight again shortly after the restart.
It came to Daniels once more, though her effort from an angle on the left was close enough to Arnold to be collected at her midriff.
Reds goalkeeper Rachael Laws had to show strength to swipe away a Hammers corner kick that was curling towards the net, with a crowd of opponents around her.
Campbell’s long throws were, as always, a consistent weapon for Liverpool and her latest just before the hour mark led to Taylor Hinds seeing a shot blocked. Fuka Nagano lifted the loose ball back into the area and Ceri Holland clipped it across goal and wide.
There was soon a triple substitution from Beard and one of those sent on, Shanice van de Sanden, fired a shot too high having got into space in the right channel.
West Ham rallied in the latter stages, flashing a ball into the area that passed unconverted, before their 85th-minute appeals for a penalty were dismissed when a Brynjarsdottir cross bounced off the arm of Koivisto.
The Reds then exerted stoppage-time pressure and only a critical block yards out by Grace Fisk prevented Katie Stengel from sweeping in from Van de Sanden’s cutback.
LFC Women: Laws, Koivisto (Roberts, 87), Robe (Taylor, 79), Bonner, Campbell (Matthews, 63), Hinds, Nagano, Kearns (Lundgaard, 63), Holland, Daniels (Van de Sanden, 63), Stengel.
Unused subs: Cumings, Kirby, Silcock, Humphrey.