Bath conceded a 14-point first-leg advantage to crash out of their Parker Pen Challenge Cup semi-final.
Tries: Marsh 2, Mignoni, Magne
Cons: Flosch 3
Pens: Flosch 4
Tries: Feaunati, Danielli, Human
Cons: Malone 2
Tony Marsh scored two first-half tries for the French side as they overturned Bath's lead within 16 minutes of a contest dominated by the hosts.
When Olivier Magne ran in for a 50th-minute try, the home side looked to have sealed their place in the final.
But two Montferrand sin-binnings led to three late Bath tries, although they proved too late to make a difference.
The Premiership side struggled on the set pieces and with their distribution and were put under pressure by Montferrand's tacklers at every turn.
Marsh marshalled his players superbly throughout the game and was deservedly rewarded with two first-half tries. His second saw him dance virtually unopposed through a shell-shocked Bath defence and slide in the corner.
Arguably the pick of the half's tries fell to Pierre Mignoni. Bath had been pushing for their first try of the afternoon only for the ball to be hoofed clear and David Bory to send Mignoni on his way.
Bath's European ambitions were effectively dashed 10 minutes after the re-start, when Magne glided over the try line.
Two quick sin-binnings for the French side gave Bath every opportunity to get back into the game. And they capitalised on it, scoring two quick tries during that spell to cut the two-leg deficit to just nine points.
First, Feaunati was judged, incorrectly by the referee, to have grounded the ball amidst a melee of forwards. And then Danielli slid into the corner after a fine passing movement from the Bath backs.
Wylie Human crossed the line in the game's final move - a score which Chris Malone duly converted. But it left Bath two points short of a place in the final.
"The damage was done in that first half," admitted Bath coach John Connolly admitted.
"We played very poorly and you can't afford to do that at this level. We were just too loose across the board and it cost us.