Albionâs first goalless draw since the opening day of the season meant they missed the opportunity to move into the top half of the WSL table.
Neither goalkeeper had much to do on an afternoon when both teams enjoyed good spells of possession but there was a lack of quality in the final third.
Albionâs best chance came in the closing moments when defender Manuela Vanegas hit the bar with a close-range header.
Albion certainly missed top scorer Kiko Seike, who was celebrating Japanâs win in the Asia Cup final on Saturday, and the lack of a central striker forced head coach Dario Vidosic to play attacking midfielders in his front three. But a first clean sheet in five league games was a positive for Vidosic.
Albion started strongly, playing through Liverpoolâs press and dominating possession and they should have scored in the 12th minute.
Manuela Vanegas took every opportunity to break forward from defence. đˇKyle Hemsley
Marisa Olislagersâ long ball found Fran Kirbyâs run in the inside left channel and the former England player looked like she was going to aim for the far corner. She opted instead to square to the unmarked Rosa Kafaji, but her pass was behind the Sweden striker and the chance had gone.
Kafaji was involved in a lot of Albionâs first-half attacks but for all their possession the hosts didnât test Liverpool keeper Jennifer Falk enough.
And when Olislagers gave the ball away inside her own box Mia Enderby only had Chiamaka Nnadozie to beat but she wastefully fired over from 12 yards.
Nnadozie also made a good save at her near post from Ceri Hollandâs shot before the break as Liverpool grew in confidence.
Madison Haley at full stretch. đˇKyle Hemsley
Beata Olson headed a corner over from a good position early in the second half and Kirsty McLean glanced another accurate set-piece by Holland wide but from open play both teams struggled to create chances.
Dario Vidosic used his bench to freshen things up and in the last minute Albion had their best chance when Caitlin Hayes nodded a corner back into the six-yard box Vanegas hit the bar with a looping header.
There was still time for drama at the other end. Liverpool sub Aurelie Csillag's shot was only partially saved by Nnadozie and the ball rolled along the goalline for a corner which was cleared off the line by Maelys Mpome.
Albion: Nnadozie, McLauchlan (Auee 87), Hayes, Vanegas, Olislagers, Rayner (Noordam 62), Symonds, Cankovic, Kafaji (Tsunoda 73), Kirby (Tvedten 87), Haley (Mpome 62).
Subs not used: Poulter, Baggaley, Camacho.
Referee: Ade Soneye
Attendance: 2316