McCartney hurt his knee at training this week and is unlikely to feature as the Hammers look to bounce back from their 3-2 defeat to Liverpool last Sunday.
McCartney joins Yossi Benayoun, Andy Carroll, Ricardo Vaz Te and Alou Diarra on the sidelines and, while long-term absentee Jack Collison is back in training, he is not yet ready for a return.
After reaching third In the Premier League table, West Brom have begun to stutter, losing three consecutive matches, and Allardyce said West Ham must exploit any doubt that may have crept into their game.
"I think they are still playing well and competing very well," he told a news conference.
"I saw how unfortunate they were to lose at Arsenal last week. Only two very poor refereeing decisions cost them the game so they may well have got something against Arsenal.
"At this moment in time, they are still playing very well but results have not matched the performances they have given. Their home form has been very good this year.
"Three defeats on the trot may put a little bit of doubt in their players and if that's the case we have to try and exploit that.
"We have our own problems with injuries so we have to rely on the players we have available to give their best again like they did against Liverpool and I hope that will be enough to get us a result at West Brom."
Despite the injury toll West Ham are still in 11th spot, and picking up points during the crowded holiday period was crucial in ensuring the club kept their Premier League status in its first season back in the top flight.
"Sticking a few wins together is where you want to be over Christmas because it sends you into the New Year in a relatively comfortable position - particularly in our first year back in the Premier League. Hopefully we can overcome our injury crisis and can continue to pick up the results we've been getting this season," Allardyce said.
(Reporting by Josh Reich; Editing by John Mehaffey)