Ole Gunnar Solskjaer's side followed that up with a 1-1 draw at Wolves on Monday, but Paul Pogba spurned a great chance to earn all three points when Rui Patricio saved his penalty.
The on-field discussion between Pogba and teammate Marcus Rashford sparked debate this week, given that Rashford clinically dispatched a spot-kick to open the scoring against Chelsea.
Solskjaer has since confirmed that both players are designated penalty takers, and United were awarded another penalty in Saturday's damaging 2-1 home loss to Crystal Palace.
With the visitors 1-0 up, Rashford missed a penalty for the first time in his Man Utd career, an outcome made worse by the fact that Anthony Martial went out of his way to ensure he took it.
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United get another penalty in loss v Palace
Midway through the second half, Man United were given a clear penalty when Martial's lay-off to Scott McTominay resulted in the young midfielder being tripped inside the box.
However, Rashford was left visibly distraught when his 70th-minute spot-kick cannoned off the post and away from the danger area.
Martial sprints to give Rashford ball for penalty
As soon as referee Paul Tierney pointed to the penalty spot, Martial sprinted over to the side of the pitch (where the ball was), picked it up, ran back to the area and handed the ball to Rashford.
Despite Solskjaer suggesting he doesn't mind who takes penalties, it's clear that Martial wanted strike partner Rashford to take this particular penalty ahead of compatriot Pogba.
Rashford's penalty miss is even more crucial seeing as United went on to lose the match in stoppage time, minutes after James curled home an 89th-minute equaliser.
Who will take the Red Devils' next penalty? Rashford? Pogba? Some supporters on social media are calling for Martial himself to become the team's new first-choice from 12 yards out.
Man Utd need to bounce back from their first loss to Crystal Palace since 1991 when they travel to St. Mary's to face Southampton next weekend.News Now - Sport News