Michael Carrick, the United head coach, described the decision as “absolutely shocking” and “one of the worst I’ve seen”.
Carrick questioned how Martínez could have been sent off for perceived violent conduct when Leeds striker Calvert-Lewin escaped any censure for what he felt was a “forearm smash” on Leny Yoro in the lead-up to Leeds’ opening goal.
Carrick hinted after the game that United would appeal the red card once he had discussed the matter with club officials.
Telegraph Sport understands United have decided to follow through with an appeal. Martínez is facing the prospect of a three-match ban that would rule him out of Saturday’s crucial clash at Chelsea in addition to the home games against Brentford and Liverpool.
Any suspension would come at a terrible time for Carrick, with the United manager facing a potential defensive crisis ahead of Chelsea.
United are expected to discover on Tuesday whether Harry Maguire will face additional punishment following his red card at Bournemouth last month after being charged with acting in an “improper manner” towards fourth official Matt Donohue following his dismissal.