Dimitar Berbatov, Fabio and Rafael were all forced off before the end of the game which Palace won 2-1.
Berbatov hobbled off with what appeared to be an ankle problem, he was seen leaving Old Trafford in a protective boot.
Twin brothers Fabio and Rafael both had fitness problems.
The trio are concerns ahead of United's league trip to Aston Villa on Saturday evening, but the club have yet to make a diagnosis on their fitness.
United said on their official website: "We've been in touch with the medical staff at Carrington and unfortunately it's too early to assess the injuries sustained last night by Dimitar Berbatov, Fabio and Rafael.
"Sir Alex will, however, be in a position to reveal more when he faces the press on Friday at his usual pre-match press conference."