Marc-Antoine Fortune followed up Benjamin Gavonon's free-kick in the 18th minute and the same free-kick taker's cross soon found the net to leave Motherwell needing four goals.
Other than a decent spell just after the break, they rarely looked like getting one as they succumbed to a 3-0 aggregate first-round defeat.
Motherwell manager Mark McGhee sprang a surprise by leaving out in-form teenager Jamie Murphy and employing an unfamiliar 3-5-2 formation.
Chris Porter, Stephen Craigan and Stephen Hughes all returned after being unavailable for Saturday's 2-1 win over St Mirren, with Marc Fitzpatrick and John Sutton joining Murphy on the bench.
McGhee perhaps wanted Murphy's pace to trouble Nancy if they tired in the latter stages - but he ended up throwing him on just after the half-hour mark in a move of desperation.
The Motherwell boss admitted his 4-5-1 system made life difficult for his players in the first leg, when only a Graeme Smith penalty save kept their hopes alive.
He had raised the temperature by accusing Nancy counterpart Pablo Correa of treating Motherwell with contempt in France and vowing to "kick their teeth in" - but the visitors were soon smiling.
Fir Park housed its largest home support for decades but almost 12,000 fans only experienced a couple of moments of real anticipation before the French side ruined the atmosphere.
The first came when Porter won a free-kick 25 yards out but Bob Malcolm curled it wide. Then David Clarkson's header was cleared away from the goalmouth after Stevie Hammell crossed from the left amid a promising break.
Nancy had Joel Sami carried off on a stretcher seconds later and Well might have had free-kicks for a foul and handball after the ensuing corner was punched away by Gennaro Bracigliano.
But Paul Quinn soon conceded a costly free-kick on the edge of his box when he pushed Monsef Zerka. Gavonon's curling shot was palmed away by Smith but Fortune tucked home the rebound.
And Gavonon killed off the tie five minutes later when his free-kick from wide on the left bypassed a crowded penalty box and curled into the far corner.
In between, Abdesalam Oaddou had replaced Sami in the Nancy back four, who coped easily with Well's immediate attempts to hit back.
Porter headed well wide from Quinn's cross and a looping first-time effort from Hughes dropped harmlessly into Bracigliano's arms.
Murphy then replaced holding midfielder Malcolm but Well could only threaten once more in the half when Porter's glancing volley from Hammell's cross just cleared the far post in the final minute.
More than 135 minutes of the tie had passed before Bracigliano made his first serious save, but his scramble to push the ball wide only came about when Steven McGarry's cross deflected off a defender.
The visitors had a good chance seconds later when Zerka shot over after Youssouf Hadji found him in space 20 yards out.
Motherwell, now playing a 4-4-2 system, finally began to string some passes together and a 25-yard strike by Hughes just cleared the bar.
They were using the width of the park to peg back the French side and Bracigliano unconvincingly scooped away Murphy's driven free-kick from 20 yards.
Striker Sutton replaced midfielder Keith Lasley in the 64th minute as Well moved to their usual 4-3-3 formation for the first time in the tie.
But Alfred N'Diaye almost exposed them moments later when he ran through the heart of the Motherwell team and drove just wide from 20 yards.
Nancy were now looking more likely to score but McGhee had to gamble further and brought on winger Darren Smith for centre-back Craigan.
However, Well's attacking players struggled to get the ball and Zerka missed an injury-time sitter as Motherwell's disappointing European campaign limped to a finish.