Against one of the meanest defences in European football, Rangers carved out precious few scoring opportunities in an uninspiring 90 minutes but may rue the golden opportunity passed up by Fernado Ricksen with 22 minutes gone and the scoreline still goalless.
In the group’s other match, a late Diego Forlan goal handed Manchester United a 1-0 win against Panathinaikos in Athens meaning Rangers will need to garner at least a point when the Greeks come to Ibrox on December 9 to guarantee third place in the group.
That scenario would grant the Ibrox side a parachute drop into the UEFA Cup after Christmas but it would not have been Alex McLeish’s preferred choice of European tournament.
Their Champions League exit this evening was widely predicted beforehand but it was the timorous manner of the defeat that will most have disappointed Alex McLeish.
The Rangers boss surprisingly chose to rest Michael Mols, opting instead to pair Peter Lovenkrands up front with top goalscorer Shota Arveladze.
Mikel Arteta’s injury meant Ricksen was pushed into the midfield with Mo Ross deputising at right back while Zurab Khizanishvili and Nuno Capucho both shook off the effects of flu to take their place in the starting 11.
Stuttgart, perhaps unsurprisingly for a team that hadn’t lost a home European tie for five years and 19 games, were the more confident as the match unfolded, with Andreas Hinkel and Alex Hleb in particular a constant threat down the right.
After just 34 seconds, Hleb hared down the wing and into the box only for Henning Berg to clear and minutes later Stephen Hughes was booked as Stuttgart threatened to run riot.
But, after that initial pounding, Rangers settled well and began to look more comfortable as they stroked the ball about at the back before passing up a glorious chance to go in front with 22 minutes on the clock.
Ross’ free kick was knocked down by Arveladze to the on-rushing Ricksen whose stab at goal from around eight yards out was parried well by Timo Hildebrand.
The Stuttgart stopper has only conceded seven goals in total this season but he really should have been stooping to pick out number eight on that occasion.
Two minutes later and Rangers should have been made to rue that failed attempt when the Germans missed a glaring chance of their own.
Hleb again was the instigator, shrugging off a few tame challenges before releasing Kevin Kuranyi through on goal.
The German internationalist – currently being chased by a host of interested clubs – continued until he saw the whites of Stefan Klos’ eyes but then dragged his shot well wide of goal.
Minutes later the pair re-enacted their personal duel, with Klos repelling Kuranyi’s attempt with his legs on this occasion.
All Rangers’ good work, however, was undone in the dying seconds of the first half when, in a carbon copy of the first match between the sides in September, they conceded an unnecessary free kick which led to a Stuttgart goal.
In what was clearly a pre-rehearsed routine, Hinkel rolled a short ball to Horst Heldt who in turn sent a spiralling ball across the face of the Rangers’ box.
It seemed a simple task for either Paolo Vanoli or Ross to clear but when the pair dithered the ball fell kindly for Timo Wenzel who sent a rasping volley past Klos.
There was little time for Rangers to respond before referee Manuel Gonzalez brought the first half to a conclusion and, as play resumed, the goal seemed to have sucked the life out of the Light Blues as they were once more penned in by Stuttgart.
Silvio Meissner rapped a drive over the crossbar before substitute Christian Tiffert slid an attempt wide of Klos’ goal as the home side piled on the pressure.
By this point and with Rangers now needing two goals to stay in the tournament, Mols had joined Arveladze up front and, shortly after, Egil Ostenstad’s arrival meant the Ibrox side now had four strikers on the pitch.
It was the home side who continued to look the more dangerous, however, and Kuranyi headed Hinkel’s cross narrowly over the bar as Gers toiled to a cacophony of shrill whistling from the Stuttgart support.
Chris Burke’s arrival with 10 minutes to go was the last throw of the dice but even the 19 year-old wunderkind was unable to conjure up any kind of magic as Rangers’ Champions League dream fizzled out for another year.
VfB STUTTGART: 1 Hildebrand; 2 Hinkel, 6 Meira, 3 Wenzel, 21 Lahm; 15 Hleb (Centurion 72), 16 Heldt (Tiffert 50), 20 Soldo, 7 Meissner; 19 Szabics (Branco 89), 22 Kuranyi
Subs not used: Heinen, Amanatidis, Gerber, Cacau
Booked: Meissner (57)
RANGERS (4-4-2): 1 Klos; 21 Ross (Ostenstad 70), 25 Berg, 15 Khizanishvili, 18 Ball; 20 Capucho, 2 Ricksen, 27 Hughes, 16 Vanoli (Mols 55); 26 Lovenkrands (Burke 80), 7 Arveladze,
Subs not used: McGregor, Emerson, Smith, Gibson
Booked: Hughes (4), Lovenkrands (77)
Man of the Match: Henning Berg