Albion bowed out of the Subway League Cup after WSL2 leaders Charlton clung onto Mary McAteerâs first-half goal to claim a notable scalp.
West Hamâs win over Southampton means they canât be overtaken at the top of Group C.
After a poor first half Albion improved when Dario Vidosic made four changes at the break.
Caitlin Hayes hit the post and Charlton keeper Anna Pedersen produced some fine saves when required as Albion dominated the second half but couldnât penetrate a determined and organised defence.
Maelys Mpome brings the ball out of defence. đˇKyle Hemsley
With Sundayâs Amex date against Leicester City in mind, Vidosic changed ten of the players on duty for last Sundayâs 1-1 draw against Liverpool with only Rachel McLauchlan, again playing on the left, keeping her place.
Charlton gained in confidence as the first half progressed although the 20th-minute goal with which they took the lead was poor from Albionâs perspective as McAteerâs cross from the left-hand side bounced between Maelys Mpome and keeper Sophie Baggaley and into the net.
Baggaley bailed Jorelyn Carabali out eight minutes before the break when the defender passed to the unmarked Emma Bissell on the edge of the box. Bissell's shot was too close to the Albion keeper who made a good save.
Albionâs best moment came in stoppage time when Mpome met Fuka Tsunodaâs corner with a looping header that Pedersen had to turn over the bar at full stretch.
Skipper Maisie Symonds was among those who came on for the second half and there was an enforced switch eight minutes into the second half when Tahirah Heron had to be stretchered off. Moments later Bissell nearly caught out Baggaley with a cross-shot from deep on the left which clipped the crossbar.
Rachel McLauchlan goes past Keira Flannery. đˇKyle Hemsley
Albion then began to exert some control and Hayes rattled the post with a shot from the edge of the box. The rebound fell to Carabali but from an angle on the corner of the six-yard box her shot drifted disappointingly wide of an empty goal. Symonds then tested Pedersen with a powerful strike from 30 yards which the Charlton keeper tipped over at full stretch.
Pedersen showed great reflexes again to keep out Hayesâ volley after Fuka Tsunodaâs free kick picked her out. From the corner Emilie Gayâs close-range shot was cleared off the line as Albion stepped up their efforts.
Hayes was pushed up front for the final 15 minutes and she forced Pedersen into another save from a header but Charlton held on.
| P | W | D | L | F | A | Pts |
West Ham | 3 | 3 | 0 | 0 | 12 | 2 | 9 |
Albion | 4 | 2 | 0 | 2 | 6 | 3 | 6 |
Charlton | 3 | 2 | 0 | 1 | 5 | 5 | 6 |
Southampton | 3 | 1 | 0 | 2 | 1 | 8 | 3 |
Portsmouth | 3 | 0 | 0 | 3 | 0 | 6 | 0 |
Albion: Baggaley, Mpome (Hayes 45), Carabali, Auee, McLauchlan (Symonds 45), Heron (Warren 53), Tsunoda, Gay, Noordam, Kafaji (Camacho 45), Martin (Milner 45).
Subs not used: Nnadozie, Poulter, Balmer.
Attendance: 566