Group E / Vfb Stuttgart 1 Rangers 0: The home side's 1-0 victory in the Gottlieb Daimler Stadium booked their place beyond the group stage at the first time of asking but all Rangers will have to play for when Panathinaikos come to Ibrox next month is a place the UEFA Cup.
Rangers' overall performance reflected their pre-match long-shot odds as the Germans never looked like surrendering a lead handed to them in first-half stoppage time by Timo Wenzel.
The first real chance of the game fell to Rangers in the 22nd minute and it took a fine save from home 'keeper Timo Hildebrand to deny Fernando Ricksen.
The shot was on target but Hildebrand thrust out a leg to divert it behind and Stuttgart almost broke the deadlock seconds later from a swift counter attack but Kevin Kuranyi spurned his opportunity .
It looked as though Rangers had survived a spell of pressure to go in level at the break but they were beguiled by a clever free kick move after Imre Szabics was fouled 30 yards in front of goal.
Wenzel was one of the candidates to take the free kick but instead ran over it before scampering into the box when Paolo Vanoli went for the delivery the ball ended up bouncing off the Italian's shoulder for the Stuttgart number three to volley past Sefan Klos into the net.
Rangers had few chances to equalize in the second half as they put Michael Mols on as an extra attacker.
Overall Stuttgart were simply too strong and held on for the victory that confirmed their place in the knockout stages for the very first time.
Rangers must avoid defeat at home to Panathinaikos in their final game to book a consolation place in the UEFA Cup.
VFB STUTTGART: Hildebrand, Hinkel, Meira, Wenzel, Lahm, Meissner, Soldo, Heldt (Tiffert 49), Hleb (Centurion 73), Szabics (Branco 89), Kuranyi. Subs Not Used: Heinen, Amanatidis, Gerber, Cacau. Booked: Meissner. Goal: Wenzel 45.
RANGERS: Klos, Ross (Ostenstad 70), Berg, Khizanishvili, Ball, Hughes, Vanoli (Mols 55), Capucho, Ricksen, Arveladze, Lovenkrands (Burke 80). Subs Not Used: McGregor, Emerson, Gibson, Smith. Booked: Hughes, Lovenkrands.
Referee: Manuel Gonzalez (Spain).