Martial and Lingard were not present in the squad named by Rangnick on Sunday, and there has been speculation surrounding the duo's future ahead of the January transfer window.
However, the German has said that two injury problems have forced the pair to miss out.
Rangnick, speaking to MUTV ahead of the match, said that Lingard "felt pain" before Saturday's training session, while Martial signalled that he had picked up an issue at the end.
The club's new interim manager named an unchanged side for the clash against Palace, with Cristiano Ronaldo in the team despite concerns over a knee problem.
Rangnick is expected to rotate his squad for next week's Champions League clash with Young Boys, as the 20-time English champions have already advanced to the last-16 stage of the competition as section winners. body check tags ::