Winston Reid and Pedro Obiang failed to finish the Premier League encounter at the London Stadium, while Michail Antonio played the full 90 minutes before being diagnosed with a hamstring issue.
Bilic fears Antonio will have to withdraw from the England squad ahead of their upcoming internationals against Germany and Lithuania due to the problem, warning the West Ham treatment room is set to become busy.
Bilic said: "Winston Reid [had to] to come out because of a conductor problem. Then Pedro, it was a challenge on his ankle.
"And now it looks like Michail [Antonio] won't be able to go with the England squad.
"[Antonio] felt something. He played the whole game but the medical team have told me now. He didn't limp off, though, so we will see tomorrow."
However, there was some positive news regarding the fitness of forward Diafra Sakho, who should return to training on Monday after nearly four months out with back and hamstring issues.
"We have Diafra Sakho who is getting stronger and stronger and he will start training with the PL2 squad next week," West Ham's head of medical and sports science Stijn Vandenbroucke told the club website.
"We work closely with Academy Director Terry Westley to ensure we can introduce returning players to controlled sessions, and Diaf will train with the PL2 squad for two weeks before he returns to training with the first team."