Now they aim to put things right in one of the toughest tests of the season.
The Seagulls, 1-0 up and dominant before losing 2-1 at home to London City Lionesses the previous week, suffered an even worse collapse at West Ham.
They were 2-0 up going into the 83rd minute after superb goals from Kiko Seike and Manuela Vanegas.
But two errors by star goalkeeper Chiamaka Nnadozie, who had earlier produced a stunning save from a free-kick, helped West Ham back into the match.
They grabbed a late winner through Viviane Asseyi from a rebound after Nnadozie had made a reflex save.
Albion now prepare to face Arsenal at the Broadfield Stadium on Sunday (2.30pm).
Interim boss Chris Roberts saw his side play some sparkling football in the London City game and hit both posts before falling behind.
They were less impressive at West Ham but seemed to have the game under control after Vanegas scored on 63 minutes.
Following her own strong tackle, she surged forward, stepped inside a defender and arrowed home an unerring finish.
Roberts said: “We are gutted. Two goals up, ten minutes to go and we lose the game.
“It’s painful, something we will have to take on the chin.
“Credit to them for getting back in. We have probably opened the door.
“Two very avoidable goals and then, when you go 2-2, you are under a lot of stress in terms of momentum.
“Until the first (West Ham) goal went in, I felt really comfortable.
“We are 2-0 up and I felt the only team who were going to get another goal at the time.
“A really hard pill to swallow. Something we will have to learn from and it has cost us.”
Nnadozie misjudged a cross by Ffion Morgan and only helped it into her own net and then made an ill-advised exit from her area as Shekiera Martinez levelled.
Her excellent save late on led to Asseyi forcing home the rebound.
The afternoon had started well for Albion, who are currently seventh in the table, and Seike’s goal was another stunner.
Her run was picked out by a pinpoint long by Moeka Minami and she carefully guided a lob over the goalkeeper for her sixth goal of the season.