Ole Gunnar Solskjaer's side are already playing Paris Saint-Germain without 10 first-team stars.
And he was forced to replace Bailly with Diogo Dalot, 19, after just 35 minutes following a late challenge from Marco Verratti.
Romelu Lukaku got United off to a dream start as he latched onto a loose pass to round Gianlugi Buffon and make it 1-0.
Juan Bernat hit back from PSG following a mistake from Bailly but Buffon's fumble gifted Lukaku a second on the half-hour mark.
United went in at the break 3-2 down on aggregate, knowing one more would earn them a spot in the quarter-finals on away goals.
Solskjaer has remained positive in the build-up despite a growing injury crisis.
But he will be concerned about Bailly, 24, going forwards as he tries to keep up momentum from a super first few months in charge.
Nemanja Matic, Ander Herrera, Juan Mata, Anthony Martial, Jesse Lingard, Matteo Darmian, Alexis Sanchez, Antonio Valencia and Phil Jones all missed the clash.
And Old Trafford chiefs will be keen to get men out of the overflowing treatment room and back on the field with a top-four spot now a real possibility.
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