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 will discover this week 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.
The England defender was suspended for the Leeds game but runs the risk of also being banned for the Chelsea game if found guilty of the charge.
With Matthijs de Ligt still sidelined with a back injury that has kept him out since November, there is a danger of Carrick being without his three first-choice centre-backs against Chelsea.
Victory against Leeds and Chelsea would have seen United open up a 13-point lead on Chelsea, who are currently in sixth, outside the five Champions League positions.
But United’s lead over Liam Rosenoir’s side would be cut to just four points were they to lose at Stamford Bridge.
United were also missing midfielder Kobbie Mainoo because of injury against Leeds and it remains to be seen if he will be fit for Saturday.
The Martínez episode is the latest in a series of decisions that United feel have gone against them this season. The club lodged a formal complaint with Professional Game Match Officials Limited, the referees’ governing body, last month after finally running out of patience in the wake of a controversial 2-2 draw at Bournemouth.
Old Trafford officials were furious that referee Stuart Attwell refused to award Amad Diallo a penalty, moments before Ryan Christie scored for Bournemouth, when Amad appeared to have his shirt pulled by Adrien Truffert but Attwell and the VAR did not give a foul.
United will learn more about Carrick now than past three months
Manchester United will probably have taken plenty of heart from the way Chelsea folded against Manchester City in the second half at Stamford Bridge last Sunday.
But those grounds for encouragement suffered a hit 24 hours later on a troubling evening at home to Leeds when a 2-1 defeat not only underlined the lack of depth in United’s squad but deepened their defensive crisis.
United would have taken a 10-point lead over sixth-placed Chelsea into Saturday’s game at Stamford Bridge had they beaten Daniel Farke’s team, but the gap will be reduced to just four points if they lose at the weekend.
It is a ground at which United have often struggled, going back decades. They have won there just twice in the Premier League since 2002 and, while Liam Rosenior’s side are hardly in form themselves, Michael Carrick has entered the most testing period of his short reign to date.
The boos that rang out at half-time at Old Trafford with Leeds 2-0 up, dominant and on course for a first league victory at their bitter rivals for 45 years felt both harsh and unhelpful given the job Carrick has done steadying the ship after Ruben Amorim’s sacking in January.
But United’s hierarchy are probably going to learn more about Carrick and his credentials in this period to follow than the three months that have preceded it. It may help to inform opinions on the former midfielder as they prepare to make a decision on the managerial front at the end of the season.
Carrick has had his fair share of luck since taking over, but that appears to have dried up in the last three weeks with injuries and the contentious decisions that went against his side in the 2-2 draw at Bournemouth and defeat by Leeds.
The first half on Monday was the poorest of Carrick’s tenure, much worse than in the 2-1 defeat at Newcastle last month when a rusty United were also way below their best and looked undercooked after so little football this season.
United remain in a very strong position to qualify for the Champions League but defensive problems have come at a bad time and the loss of Kobbie Mainoo in the 72 hours before the Leeds match was also a blow.
What followed, with Manuel Ugarte struggling alongside Casemiro, highlighted why revamping central midfield is the priority in this summer’s transfer window. Carrick will be desperate to have Mainoo back for Chelsea.
Losing Lisandro Martínez for three matches for violent conduct for pulling Dominic Calvert-Lewin’s ponytail will be even more keenly felt should Harry Maguire end up being given with a new suspension and miss the Chelsea match.
The England defender was suspended against Leeds after his red card at Bournemouth but faces the threat of an additional one-match ban from the Football Association for mouthing something at fourth official Matt Donohue at the Vitality Stadium following his dismissal.
Telegraph Sport revealed on Tuesday that United will appeal Martínez’s red card. Yet unless the club are successful on that front Carrick could yet be without his three first-choice centre-backs at Stamford Bridge since Matthijs de Ligt is still sidelined with a back complaint that has kept him out since November.
That would mean the manager would be likely to pair youngsters Leny Yoro and Ayden Heaven in the heart of the defence.
Diogo Dalot and Bryan Mbeumo are expected to come back into the starting XI but the latter has struggled for form, as has Amad Diallo, since they returned from the Africa Cup of Nations in January. Matheus Cunha, similarly, needs to show greater consistency.
Carrick faced criticism in some quarters for not changing things sooner against Leeds but it is also worth remembering he was being praised for his positive and proactive substitutions not too long ago.
United are still in the box seat when it comes to the race for Champions League qualification outside the top two but they must emerge from this sticky spell.
