Bridge (calf), El-Abd (calf) and Marcos Painter (calf) all missed Saturday's 3-0 derby defeat at Crystal Palace.
Painter has already been ruled out of the trip to The Valley and Poyet's back four headache has been compounded by a ban for Lewis Dunk for his early red card at Palace.
The Seagulls ended up with Liam Bridcutt at left-back at Selhurst Park with Bridge and Painter sidelined, Inigo Calderon switched to centre half following Dunk's dismissal and Andrea Orlandi forced off by a suspected broken rib after he had been moved from midfield into the defence.
Poyet revealed to The Argus: "Marcos has got a small tear in his calf, so he is out for a while, between two or three weeks.
"Now it's going to be a case of getting Bridgey back or playing Calde. Then at centre half we need to make sure the medical staff produce something and get Adam El-Abd back.
"Wayne has got the biggest chance to be fit. Adam was allright, then on Thursday he didn't feel right and we had to stop him. We need to make sure they are there. Sometimes you need to push it. Let's hope it can happen."
Dunk lost control of the ball and brought down man-of-the-match Yannick Bolasie. Palace cashed in with goals either side of half-time by former Seagull Glenn Murray, the second a penalty, and another penalty from Owen Garvan.
Poyet said: "He (Dunk) was too casual. You need to deal with the situation. He is young and I hope he learns from it."
Albion's first defeat in eight games dropped them to eighth, two points outside the play-offs.