Midfielder Enock Mwepu lasted just 28 minutes at the Hawthorns as the Zambia international sustained a hamstring injury during the first half.
Debutant Odel Offiah, who made an encouraging first outing on the right flank, was also forced off early in the second half with a ankle problem.
Mwepu's injury in particular is a problem for head coach Graham Potter as he is already without key midfielder Yves Bissouma who is on international duty with Mali at the Africa Cup of Nations.
Of Mwepu's injury, Potter said after the game: “I don’t think it’s too serious with the caveat that I have just come from the changing rooms.
“He didn’t feel anything go, it was more tightness I think, so fingers crossed for the next 24 to 48 hours.
“I think it was more precaution that he came off. We will see how he is."
Offiah, 19, looked a powerful and athletic figure at the Hawthorns but Potter said his after was cut short due to an ankle problem.
"He went over on his ankle but I have not had the full debrief from the medical department. He did fine. As you would imagine it was a tough afternoon in the third round of the FA Cup.
"If you take this competition lightly you can come a cropper. Our attitude and our mentality was good and it helped him and I thought he did well."