Hearts took their French leave from the UEFA Cup when they surrendered a first-leg advantage to succumb tamely to Bordeaux at Tynecastle.
It was a hugely disappointing night for the Edinburgh side after such a remarkable win in France.
Craig Levein's tactical gamble of playing with just one striker and defending the first-leg lead backfired and they could have lost more heavily.
Hearts, without skipper Steven Pressley through injury, made their intentions clear from the start as they sat deep in a bid to deny Bordeaux space.
But the tactic backfired when they lost a goal after only eight minutes. Jean-Louis Valois gave the ball away in midfield and Alberto Riera beat Craig Gordon with a swerving shot from 30 yards that found the top corner.
Hearts could have been three goals down by half time as Bordeaux hit woodwork twice with the Edinburgh side almost paying the price for being too cautious.
Phil Stamp had a rare chance for Hearts when Neil MacFarlane put him through and Urlich Rame failed to hold his shot but Bordeaux scrambled the ball clear.
But the French side were unlucky not to extend their lead in the 26th minute when Kevin McKenna headed out a Riera corner only for Jean-Claude Darcheville to volley against the crossbar with Gordon well beaten.
Nine minutes later, another McKenna clearance fell to Pascal Feindouno but an alert Gordon touched his right-foot volley onto the post.
Stamp had the ball in the net for Hearts shortly before half time but the goal was disallowed as he had strayed marginally offside.
Hearts were more positive in the second half and Mark de Vries had a decent shot on the turn but Rame was well positioned to save.
But Bordeaux snatched the all-important second goal in the 66th minute when Marouane Chamakh raced down the left and cut the ball back for Feindouno to produce an accomplished finish.
It left Hearts needing two goals to go through and they almost snatched one back immediately but Stamp lashed his effort over the top from just ten yards.
Substitute Stephen Simmons then forced an acrobatic save from Rame as Hearts went all out to try and salvage the tie.
Darcheville should have scored at the other end when he rounded Gordon but, from a tight angle, found only the sidenetting.