With 15 minutes remaining, substitute Keyrol Figueroa thought he had levelled with a charge down on goalkeeper Awesu.
The forward blocked a clearance leaving the ball to loop towards goal, but appeals that the chance had crossed the line were waved away by the match officials.
Liverpool responded with Nyoni kept out once again after being released forward by Kieran Morrison, while Carter Pinnington saw a header from a corner ball saved and scrambled away.
West Ham's Emeka Adiele was then dismissed in the third minute of stoppage time for a second bookable offence with the game coming to a close.
Barry Lewtas' outfit, though, were not to be denied a leveller in minute 95 to earn what was a deserved point on home soil.
A free kick swung into the box by Morrison found its way to Lewis Orford, who inadvertently turned home into his own goal via a header to restore parity in what was the last of the action.
**Team**
**Liverpool:** Davies, Mabaya, Jonas, Pinnington, Nallo, McConnell (Laffey, 30), Kone-Doherty, Nyoni, Young (Ngumoha, 63), Morrison, Pilling (Figueroa, 79).
**Subs not used:** Misciur, Spearing.
**Next up**
The Reds will take on Brighton & Hove Albion next in Premier League 2 on Sunday April 6, with Liverpool travelling to the Amex Elite Football Performance Centre in a 4pm BST kick-off.