A late header by Linas Pilibaitis gave Lithuanians Kaunas a shock 2-1 victory over Rangers in the Champions League second qualifying round second leg on Tuesday.
Rangers, beaten by Zenit St Petersburg in last season's UEFA Cup final, went into the game under threat of an embarrassingly premature exit from European competition after a goalless home draw in Glasgow last Wednesday.
Their worst fears were then realised when Pilibaitis headed in a corner for the Lithuanian champions with three minutes remaining.
Manager Walter Smith said Rangers paid the price for an "extremely poor performance".
"It is ridiculous you can reach a European final and then get knocked out in the first game of the next season but that's the way it has happened," Smith told BBC radio.
"We've got no excuses."
Defeat at this stage of Champions League qualifying means the Scottish team do not even drop into the UEFA Cup.
Rangers looked on course to progress when midfielder Kevin Thomson netted in the 33rd minute, breaking on to a Nacho Novo pass to score with a low shot through the legs of goalkeeper Marian Kello.
Defender Nerijus Radzius equalised for hosts Kaunas 10 minutes later with a fierce free kick which flew over the wall and beyond the right hand of goalkeeper Allan McGregor.
Kaunas are now likely to face AaB Aalborg in the third qualifying round later this month. The Danish champions lead Modrica of Bosnia 5-0 going into their second leg on Wednesday.
Norwegian champions Brann Bergen squeezed past Ventspils on away goals in Tuesday's other match.
Despite a 2-1 defeat in Latvia, Brann advanced thanks to a 1-0 first-leg victory last week.
Their reward is a third qualifying round tie against Olympique Marseille.
