With the Premier League title all but wrapped up, the Red Devils are now faced with a month and a half of practically meaningless games.
Here are the player ratings for Sir Alex Ferguson's side.
David de Gea: 7
The Spanish shot-stopper could do little to prevent Demba Ba's deft volley from looping into the corner of his goal.
Apart from that he was excellent, making smart saves to deny Ramires and Juan Mata during the game.
Antonio Valencia: 6
Playing at right-back in Rafael's stead, Antonio Valencia was ironically far improved than his previous performances this year.
Going forward he offered little, but though he was caught out of position a couple of times, defensively, he wasn't that bad at all.
Chris Smalling: 6
Playing his fourth game in a little over a week, Chris Smalling could be forgiven for the odd lapse in concentration against Chelsea.
His partnership with Rio Ferdinand is an unfamiliar one, and could be the reason for Demba Ba being allowed clear passage through the middle for Chelsea's goal.
Rio Ferdinand: 6
A decent performance from Rio Ferdinand, who was quite calm in possession in comparison with some of his teammates.
Facing a barrage of boos from the Stamford Bridge faithful, the veteran defender didn't look perturbed at all.
Patrice Evra: 5
This season has been Patrice Evra's best since 2010, but the Frenchman was unfortunately a bit of a weak link for the Red Devils Monday.
He was beaten by the quicker, more skillful Oscar several times one-on-one and struggled to make much headway down the left flank.
Michael Carrick: 6
Michael Carrick was unsurprisingly one of Manchester United's better players against Chelsea in the first half—calm on the ball and offering able protection for the back line.
But as the second half wore on, fatigue began to take over as he made a couple of misplaced passes and was caught napping in possession several times.
Phil Jones: 7
A decent game for the returning Phil Jones, who has been sorely missed since going down injured in late February.
The Englishman was one of his side's most reliable players, completing 91 percent of his passes in a congested midfield compared to Carrick's 81 percent (via WhoScored.com).
An absolutely horrible outing for the Portuguese winger, who was lucky to remain on the pitch past halftime.
At one stage of the first half, it seemed like a miracle whenever his first touch didn't let him down. Disappointing considering his decent displays before the injury he picked up against Chelsea in the 2-2 draw in March.
Tom Cleverley: 5
Not a great game for the Englishman, who was curiously played on the left wing instead of his usual central role.
He failed to create anything meaningful from out wide, even if his passing and movement was quite good.
Danny Welbeck: 7
Probably Manchester United's best player, even if tired legs meant he was unable finish the game on the pitch.
The Englishman seemed like a man on a mission to impress in the first half, darting back and forth across the pitch with a youthful exuberance and displaying fantastic skill.
Javier Hernandez: 6
If it weren't for an absolutely stunning save from Petr Cech in the second half, Javier Hernandez may now be being hailed as United's hero.
But as it is, the Mexican can feel proud of a determined, above-average performance, even if he has nothing to show for it.
Robin van Persie: 5
What on earth has happened to the Dutchman? The striker could have scored a brace in the final 30 minutes of the game, but his finishing let him down not for the first time this year.
Ryan Giggs: 6
The age-defying Welshman tried his best to impact the game, but a few sublime passes were not enough.
Ashley Young: N/A
With only 15 minutes to shine, it would be unfair to give Young a rating, even though he was rather disappointing yet again.
Who impressed you the most for the Red Devils? Who was lacklustre?