Allardyce was without seven injured players - including Ricardo Vaz Te, Yossi Benayoun, Andy Carroll, Jack Collison and Mohamed Diame - for the Premier League clash at The Hawthorns.
But he was full of praise for the way his below-strength line-up fought to claim a share of the spoils against an Albion side who had won six of their previous eight home games this season.
Allardyce said: "January will be important to us. We want to continue where we've got to already and push on from there if we can.
"We don't want to slip down the league and lose matches. Being without two or three players is okay but six or seven is far too many for us.
"We coped well at West Brom but I'm not sure just how long we will cope if we have them out too long.
"We've got some really good players like Vaz Te, Benayoun, Carroll, Collison, Diame, all attacking players with flair, who were missing.
"But we earned our point with a good, honest, solid performance."