With Juventus beating Valencia in the other Group H match, United knew victory against the Swiss champions - a side they beat 3-0 in Switzerland - would have secured progress with a match to spare.
But Mourinho's underperforming side lacked creativity, cohesion and confidence against a Young Boys side displaying all those characteristics, only for Fellaini to secure a lucky 1-0 win and progress to the knockout phase in stoppage time.
The United manager's frustration had been growing throughout the match and his angry celebration said it all as he kicked one water bottle carrier and threw another into the floor.
Victory meant United head to Valencia next month with progress assured, but Tuesday's performance raises more questions than answers given their tepid response to Saturday's goalless draw with struggling Crystal Palace.
The Champions League is back! Headlining our live blog action tonight is Manchester United vs Young Boys and Lyon vs Manchester City. City have nine points from their opening four games and another point here would guarantee their progress to the last 16, despite that slip up against Lyon when these two sides met at the Etihad. United's position is a little more precarious, and they cannot afford to slip up against the Group H stragglers if they are to come through their three-way battle with Juventus and Valencia, who meet tonight in Turin. Harry will be along shortly with all the team news and build-up to kick-off at 8pm GMT.
Yes, the Champions League is back! It is a Tuesday night, both Manchester clubs are in action and there are a host of other games on as well.
As you can see the Manchester City team is out already and we are expecting confirmation of the three other starting lineups imminently, so let's get to it...
After Manchester United's dramatic win in Turin, a victory tonight could take them through to the knockout stages should Valencia fail to win at Juventus tonight. That is also an 8pm kick-off, and we will have score updates of all the fixtures being played in the competition this evening at half-time and after the full-time whistle blows...
BSC Young Boys are Manchester United's opponents this evening. Based in Bern, they won the Swiss Super League last season and are already 16 points clear after just 15 games this.
One of their key attacking influences is Miralem Sulejmani, who very nearly joined West Ham in 2010 while at Ajax. The Serbian winger agreed a move to England on loan, but was denied a work permit.
Aymeric Laporte may just be the best footballer in the world without a single international cap.
He starts in the country of his birth tonight, and Jack Pitt-Brooke dissected how the centre-back has helped take Manchester City to even greater heights.
An interesting tactical option taken by Pep Guardiola tonight, with Kyle Wlaker seemingly on the right of a back three also containing John Stones and Aymeric Laporte.
Lyon have picked what is, for all intents and purposes, a back five, so Guardiola has gone like-for-like.
Luke Shaw's forward pass is too heavy for Jesse Lingard, but LIngard manages to just about get a toe on it which inadvertently takes it perfectly into the onrushing Rashford's path.
Rashford is one-on-one with David von Ballmoos but finds only the top of the net with his lofted effort.
Lyon work space on the right and cross towards the Dutchman who is in excellent position in the Manchester City box, but he takes his eye of his volley and it goes rather awry.
At the other end, Riyad Mahrez has an equally opportune moment but can't beat Anthony Lopes, who holds onto his shot.
