Matthew Etherington failed to make it past the warm-up with a groin problem while Dean Ashton limped off with a hamstring strain with the Cardiff showpiece just 12 days away.
Captain Nigel Reo-Coker struck a 41st-minute winner for the Hammers but the injury problems were the least Pardew needed with Hayden Mullins’ suspension appeal having failed.
Pardew had made six changes from the side which lost at Liverpool, with no starting places for the likes of Anton Ferdinand, Marlon Harewood or Paul Konchesky.
It was not the ending required by boss Bryan Robson, who would also have to put up with a small section of the home supporters calling for his head following the final whistle.
Nigel Quashie had the ball in the net in the 25th minute but was ruled offside by an assistant.
Elliott Ward headed just over for the Hammers in the 36th minute, before Reo-Coker took advantage of the Baggies’ failure to stop Bobby Zamora’s wriggly run into the box with a right-foot shot low past Tomasz Kuszczak.
: Kuszczak, Albrechtsen, Watson, Curtis Davies, Robinson, Greening, Wallwork, Quashie, Gera, Ellington, Kanu.
: Hislop, Dailly (Konchesky 73), Gabbidon, Fletcher, Scaloni, Newton, Reo-Coker, Ward, Reid, Ashton (Sheringham 23), Zamora (Harewood 71).
: G Poll (Hertfordshire).