“[Martial] didn’t want to be in the squad,” said Rangnick in a press conference after the 2-2 draw.
“He would have been in the squad normally, but he didn’t want to. That is the reason why he was not travelling with us [on Friday].”
But Martial quickly refuted the claim, adding that he would not “disrespect the fans”.
The striker posted on Instagram: “I will never refuse to play a match for Man United. I’ve been here for seven years and I never disrespected, and will never disrespect, the club and the fans.”
Martial has been linked with a move away from Old Trafford this month, with Sevilla and Newcastle reportedly keen on his services.
United led 2-0 at Villa after a brace from Bruno Fernandes before a late comeback from the hosts, capped by a goal on his debut by Philippe Coutinho.