The Magpies provided little resistance against the French side, which clinched top spot in Group D thanks to a double from Malian forward Cheick Diabate
A double from Malian striker Cheick Diabate was enough to seal first place for Francis Gillot's men, who deserved the three points after dominating for much of the contest.
The home side made the better start to proceedings, with winger Henri Saivet and midfielder Fahid Ben Khalfallah both drawing good saves from Newcastle goalkeeper Robert Elliot in the early stages.
Newcastle provided a sporadic threat in the form of Sammy Ameobi, who appeared dangerous operating from the left flank, however it was Elliot who was the busier of the two keepers, and he was forced into a fine double save just before the 20 minute mark to deny first David Bellion, and then debutant Andre Biyogo-Poko.
The visitors looked composed and patient on the ball for most of the first half, but it was Les Girondins who carried the greater threat, and they took the lead when Diabate headed home from a well placed Ben Khalfallah cross.
Bordeaux continued to control the game without really creating any further opportunities, however it was never in danger of conceding the initiative in the opening period.
Newcastle brought on Vurnon Anita - one of the stars of the recent victory over Wigan - in place of Sammy Ameobi following the halftime interval, and this did prompt an improvement in the first flings of the second half, as Shola Ameobi latched onto an excellent ball from Gael Bigirimana to force a superb reflex save from Kevin Olimpa, before Abeid curled an effort just wide of the far post.
Alan Pardew's side pressed with increasing urgency to find an equalizer, but the game was settled midway through the second period, as Diabate latched onto a through ball to slot a cool finish past Elliot and end any hopes Newcastle had of winning the group.
The game was dead as a contest following that strike, and although the Magpies did show some signs of life, they did not appear too concerned by their plight and will be pleased to concentrate solely on their Premier League form until European competition restarts in February.