Arsenal's hopes of even progressing to the second round of the Champions League, let alone attempting to fulfil their lofty ambitions to challenge Europe's best, look forlorn after another dismal, insipid and, at times, pitiful display on foreign soil.
This was another performance to add to the worrying number by Arsenal on their Champions League roadshow, or rather no-shows over the past three seasons. It was as embarrassing as their previous feeble displays at Spartak Moscow, Shaktar Donetsk, Dynamo Kiev and Bayern Munich and gave Panathinaikos their first win over English opponents.
Arsenal lacked both real quality and a cutting edge, failing to put a single shot on target.
Greek fans had pummelled the side of their coach with their fists as it negotiated the narrow streets surrounding the stadium, but inside it the home team adopted a more patient and cunning plan, playing the ball out from the back and hoping to catch Arsenal on the break.
Another hastily assembled Arsenal back four, in which Matthew Upson was given his first start of the season in place of Tony Adams, looked nervous and uncertain in the opening stages.
But just when they seemed to have settled into a rhythm, they conceded a soft goal. Karagounis dived in to head Jan Michaelsen's right wing cross into the bottom corner.
The defence shot accusing glances at each other but Arsenal's often non-existent midfield were as much to blame, allowing Panathinaikos far too much time and space to set up the move, possibly concerned that the over fussy Portuguese referee would punish any challenges with a free kick.
The defensive frailties frightened the strangely subdued Vieira into playing even deeper than usual, thus restricting the hopes of strikers Thierry Henry and Sylvain Wiltord for any decent service from which to fashion a tide-turning opportunity.
Arsenal's only crumb of encouragement in the first 45 minutes came from a fiercely struck shot from Freddie Ljungberg which dipped wide. And as a deeply disappointing Arsenal side struggled to gain possession, let alone create anything, it really should have been Panathinaikos who scored again after a piece of uncharacteristic misjudgment by Martin Keown seven minutes from half-time.
It allowed Emmanuele Olisadabe to skip clear in the box and sidestep the despairing David Seaman, only for the excitement of the moment to cause him to shoot into the side netting.
A frustrated Vieira was reduced to trying a long-range shot which rebounded off a defender for a corner that yielded catching practice for goalkeeper Antonis Nikopolidis.
PANATHINAIKOS: Nikopolidis; Henriksen, P Sousa; Vlaovic (Konstantinou 65), Michaelsen, Vokolos, Kygiakos, Basinas, Olisadebe (Kolkka 70), Karagounis (Saric 84), Fyssas.
ARSENAL: Seaman; Cole, Vieira, Keown, Pires, Ljungberg (Kanu 68), Wiltord (Jeffers 68), Lauren, Henry, Parlour (van Bronkhorst 53), Upson.
Referee: V Pereira (Portugal)