The United manager vented his anger at Martial in front of the other players in the dressing-room after leaving the Frenchman on the bench at Old Trafford.
Fans criticised the 23-year-old winger on social media on Monday after he was filmed watching his teammates in the pre-match warm-up, holding his hands behind his back and standing with one foot on a ball while they went through a series of drills.
Martial has been complaining of a bad back but it’s understood that Solskjaer was unhappy with the player’s blatant lack of effort.
He decided to send on Alexis Sanchez rather than Martial as a replacement for Marcus Rashford when the striker succumbed to an existing shoulder injury in the 65th minute.
There have been concerns over Martial’s attitude since he signed a new five-year contract at the end of January following a string of lack-lustre performances.
Martial covers an average distance of 8.45km per game, which means his attacking team-mates are covering much more ground than the Frenchman.
Eric Bailly is the only outfield player who has worst running statistics than Martial during the course of the current campaign.
Having been first-choice since Solskjaer took over in December in a front three alongside Rashford and Jesse Lingard, the former Monaco man is now firmly out of favour.
Jose Mourinho’s frustration with Martial was such that he wanted to sell him last summer, and Solskjaer too has become exasperated by the player’s approach.
The dressing-room incident took some of the focus away from goalkeeper David de Gea whose latest error gifted Chelsea an equaliser as United’s hopes of a top-four finish suffered a serious setback.
Solskjaer is expected to stand by de Gea for the remaining two games against Huddersfield and Cardiff, and teammates have been rallying round the Spaniard.
‘I don’t think we should discredit him and suddenly say he is a bad goalkeeper – he has saved us many times this season,’ said striker Romelu Lukaku.
‘We are here to support him. Mentally he is really, really strong or else he wouldn’t have been the best player at the club for seven or eight years. There is no doubting his ability.
‘It happens to strikers, it happens to midfielders and now it is happening to him. He has to learn from it. Goalkeepers always have a spell when it might be difficult.
‘He had a bad time at the start of his United career, as I remember. He was just a kid then but came through it. He did what he had to do then: turned it round, won trophies and became the best player at the club.
‘He is a leader in the dressing-room. Now it is up to us as a team to help him and trust his abilities.’
De Gea has been linked with a move to Paris Saint-Germain this summer as he enters the final year of his contract, and Lukaku stopped short of committing his future to United when asked if he will still be at Old Trafford next season.
‘Me? I don’t know,’ added Lukaku, whose agent Federico Pastorello has been discussing a move to Italy. ‘I am not here to entertain rumours. I am still under contract.’
Meanwhile, Eric Bailly may have played his last game for United after he was ruled out of the club’s final two fixtures and the Africa Cup of Nations in June and July with a knee injury.
The 25-year-old Ivory Coast defender limped out of the Chelsea game after he collided with Mateo Kovacic in the second half, and scans confirmed damage to the medial ligament in his right knee.
It was only Bailly’s sixth start under Solskjaer and he has been linked with both Arsenal and Lyon.
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