United's hopes of retaining the FA Cup disappeared with the flash of Michael Oliver's red card in the 35th minute of this quarter final.
An already uphill task was rendered almost impossible when Ander Herrera was sent off for a (harsh) second booking for a clumsy foul on Eden Hazard.
The Belgian, as he did all night, greatly exaggerated the coming-together to get the Spaniard sent off and despite a bravely valiant effort, the tie proved a (Stamford) Bridge too far for the team.
The players can take great heart from their performance, though.
There's no shame in getting knocked out by the best team in the country and a side who remain overwhelming favourites for the domestic double.
With the odds stacked against them in adversity, the Reds showed courage and commitment and kept going until the death.
Instead of the feeble surrender we saw in October and despite the numerical disadvantage, there was the heart-warming sight of a spirited late rally on the Chelsea goal.
Had Paul Pogba's 86th-minute effort crept in the corner and not narrowly wide, United would've forced extra-time and then who knows what might have happened.
In the absence of their three main forwards, the Reds summoned Marcus Rashford from his sickbed and, despite not being 100% fit, the young man was our best performer.
He almost capped a superb individual display with a goal - thwarted only by Courtois after a breathtaking counter-attack - and ran his socks off all night in a selfless showing of pace, energy and industry.
Antonio Valencia was again immense at right wing-back and there were also stellar showings from Ashley Young and Marcos Rojo - who could face FA action after a late altercation with Hazard.
This was a brilliantly feisty and frenetic encounter that lived up to its billing, with as much drama on the touchline as the pitch.
The two managers kicked every ball on the touchline and at one point had to be pulled apart by fourth official Mike Jones.
The flashpoint came when Mourinho - angered by what he interpreted as a Marcos Alonso dive - exploded with fury and clashed with Conte in a heated exchange of bad blood.
It was a feud that bubbled throughout but ended amicably with a warm handshake and embrace on the final whistle.
With our FA Cup run over, attention now turns to another cup competition as we face Rostov on Thursday for a place in the Europa League quarter-final.
Jose has always maintained that the competition - and the Champions League prize it brings - has been of priority for him and the team this term.
Despite Monday's disappointment, there are lots of positives to take ahead of the run-in which could still end in European glory in Stockholm in May.