Glasgow failed to become the first Scottish side to win in France in the Heineken Cup despite a gutsy display.
Bourgoin 16 (6)
Pens: Boyet (2), Carmona
Glasgow 3 (3)
The visitors opened the scoring with a penalty from Dan Parks, but that proved to be their last points of the game.
Benjamin Boyet levelled moments later before moving Bourgoin into a 6-3 lead at the interval with another penalty.
The fly-half was also the creator of the night's only try in the second half - making a lethal break before looping a long pass to try scorer David Janin.
Glasgow were unfortunate not to add to Parks's earlier penalty and came within a whisker of a first-half try.
A Colin Shaw chip to the right-hand corner left Bourgoin's defence in disarray.
Graeme Morrison emerged from the subsequent melee of players, but the try was ruled out after being referred to the television referee.
Despite that setback, the Warriors pushed their opponents to the final whistle but were unable to find a way through.
Glasgow assistant coach Sean Lineen:
"The result does not reflect the whole story. We had so many problems in the build-up to the match - yet the guys came up with a performance which was bursting with guts and bravery.
"The raw young lads who came in, John Beattie and John Barclay, were absolutely immense and we could not have asked for an ounce more effort from them.
"There is no doubt in my mind that we did enough to come away with a bonus point, but it wasn't to be.
"If we can show the same level of commitment during the rest of the campaign, we can make an impact."
Bourgoin: A. Forest; Janin, Bousses, Giorgadze, Coux; Boyet, M. Forest; Milloud, Montagnat, Peyron; Pape, Pierre; Diotallevi, Baluc-Rittener, Jooste.
Replacements: Davis for Boyet (71), Cardinali for Peyron (63), Monzeglio for Diotallevi (29).
Not Used: Khinchagishvili, Del-Fava, Carmona, Campeggia.
Glasgow: Shaw; O'Hare, Morrison, Henderson, Craig; Parks, Beveridge; Tckachuk, Lawson, Harrison; Hamilton, Barker; Dearlove, Barclay, Beattie.
Replacements: Pinder for Beveridge (58), Thomson for Lawson (63), Hayter for Beattie (45).
Not Used: Corsar, Turner, Gregor, Staniforth.
Ref: Dave Pearson (RFU).