Leading 1-0 from the first leg, Kaiserslautern hit back to win 3-0 with goals from Miroslave Klose Andreas Buck and Vratislav Lokvenc who Advocaat himself tried to sign from Sparta Prague in the summer.
The Little General is used to springing personnel surprises in European games but the omission of the influential Dutch pair of Michael Mols and Ronald de Boer appeared to have been a forced change rather than through choice.
And with Barry Ferguson and Giovanni van Bronckhorst also missing due to suspension and injury respectively it was always going to be a difficult task for the Light Blues to hold on to their 1-0 lead from the first leg.
That is how it proved in the early part of the game with Rangers struggling to get to grips with the game, particularly in the middle of the park. Kaiserslautern took the match by the scruff of the neck and dominated proceedings.
And it took the Bundesliga side just seven minutes to get their noses in front. Klose got the ball on the right hand side and with some neat footwork he got past Scott Wilson before neatly lobbing the ball over Stefan Klos.
German ‘keeper Georg Koch, who was outstanding in the first leg at Ibrox, said before the game that if any Rangers player had to score then he hoped it would be his fellow countryman and former team-mate at Fortuna Dusseldorf, Jorg Albertz.
And that was almost the case in the 18th minute when the powerful midfielder was one-on-one with Koch but it was the same outcome as was often the case at Ibrox with the man between the sticks keeping his old pal out.
Albertz was next to have a crack at goal but a rare header from the Big German was well held by Koch who stopped the ball on the line.
Klos was in fine form at Tynecastle on Sunday and he carried that into the Fritz-Walter Stadium this afternoon. Twice within the space of a minute he made excellent saves from Youri Djorkaeff to deny Kaiserslautern a further goal.
Advocaat would have been a worried man at half-time and he switched things around at the break, bringing on frontmen Michael Mols and Neil McCann at the expense of Fernando Ricksen and Kenny Miller who appeared to have picked up a knock.
Mols looked lively immediately after coming on but it was Andreas Brehme’s side who scored the next goal – in the 64th minute – which proved vital. Rangers were caught out on the counter-attack with a long ball out of defence which Buck latched onto, he ran half the length of the park before calmly slotting past the helpless Klos.
It was all or nothing for Rangers and Advocaat threw on Billy Dodds for the last 15 minutes which meant the Light Blues had three out-and-out strikers on the pitch.
But with that move there was always a danger Kaiserslautern would get another goal and that proved to be the case. In the 79th minute Bulgarian Dimitrios Grammozis did brilliantly on the left hand side, turning Claudio Reyna and his cross was headed in by Lokvenc.
It was yet another disappointing end to a European campaign for the vociferous travelling Light Blue legions who will have to wait another year in a bid to see their team playing football on the continent after Christmas.
RANGERS: Klos, Ricksen (McCann 45), Numan, Amoruso, Konterman, Wilson, Tugay (Dodds 76), Albertz, Reyna, Miller (Mols 45), Wallace Subs (not used): Christiansen, Vidmar, Porrini, De Boer
KAISERSLAUTERN: G Koch, H Koch, Yakin, Ramzy, Buck, Komljenovic (Strasser 4), Djorakeff, Grammozif, Hristov (Basler 87), Klose (Marschall 69), Lokvenc Subs: Weidbnfeller, Schjomberg, Reich, Adzic
Bookings: Kaiserslautern – Marschall (70)
Referee: Knud Erik Fisker (Denmark)