The 26-year-old France international was missing in action in the 2-2 draw at Villa Park, with United naming two goalkeepers among their substitutes as the likes of Cristiano Ronaldo and Marcus Rashford also missed out due to injuries.
Martial has asked to leave Manchester United in the January transfer window in a bid to get regular game time elsewhere.
Speaking to reporters after the game on Saturday, Rangnick said: "He didn't want to be in the squad.
"He would have been in the squad normally but he didn't want to and that's the reason why he was not travelling with us yesterday."
But Martial insists he will never refuse to play for Manchester United when called upon.
"I will never refuse to play a match for Man United," Martial said on Instagram.
"I've been here for seven years and I never disrespected and I never will disrespect the club and the fans."
Martial has started just two Premier League games this season, and has made 10 appearances in all competitions.
He is yet to feature since Rangnick took over from Ole Gunnar Solskjaer in December.
Martial joined United from AS Monaco for £36m in the summer of 2015 and has gone on to score 79 goals in 268 games for the Red Devils, winning one FA Cup, one League Cup and the Europa League.
