Allardyce was without seven first-team players and only able to name six substitutes at the Hawthorns.
But he was full of praise for the way his side fought to claim a share of the spoils.
Allardyce said: "You could probably say it's seven injuries because we haven't seen Alou Diarra since he joined us because he tore a thigh muscle.
"That, on top of the other six, made it very difficult for us to come here. That's why we only had six subs on the bench.
"The only two really recognised players who played any part, we put on at the end, Modibo Maiga and James Tomkins. The rest of the lads are development squad players.
"But we've earned our point. You know when you've got that many injuries, you're always worried as a manager because you wonder whether you're team's going to be able or capable of holding out.
"Certainly on that performance, the way they defended, we didn't create as much as we wanted.
"We tried as hard as we could to do that but our defensive qualities today were exceptionally good."