Rangers lost out on the consolation of even a UEFA Cup place as Panathinaikos taught the home side a lesson in finishing.
Despite the boost of scoring first through Michael Mols the home team were soon back on level terms after a wonderful strike by Raimondas Zutautas.
The Greek side added second-half goals through a superb shot from Angelos Basinas and a well-taken goal by Michael Konstantinou as Rangers once again failed to make an impact in Europe.
The opening 20 minutes were very tentative with neither side wanting to make a mistake. A dipping cross by Chris Burke was headed away by Yannis Goumas before the young winger could only head weakly into the arms of keeper Antonios Nikopolidis.
Rangers took an unexpected lead when Michael Ball's dangerous cross was headed into the top corner of the net by Mols.
Panathinaikos looked rattled at this stage with Nasief Morris giving away possession to Nuno Capucho on the edge of the box but the Rangers striker was unable to take advantage.
The Greek side equalised shortly after when Zutautas struck a superb 25-yard effort which beat Stefan Klos all ends up after Markus Munch had created the chance.
The second half was totally dominated by Panathinaikos. The visitors nearly went ahead when Miltiadis Sapanis was denied by a brave block from Klos.
A superb driving run by substitute Joel Epalle led to Konstantinou striking the post from 20 yards before the visitors deservedly went ahead for the first time in the match.
There appeared little danger when Basinas picked up a loose ball nearly 40 yards from goal but the midfield player unleashed a shot which Klos knew little about before it ended up in the net.
Ibrox was silenced as the Greeks ended the game as a contest with ten minutes remaining. Konstantinou beat the offside trap before clinically shooting low past Klos to leave Rangers once again without European football before Christmas.