It was simply a game too far for McLeish’s squad. Missing seven players – most of whom are utterly key – they were unable to produce the level of performance necessary at this level.
They were leading in what was their 140th European match when Michael Mols headed them in front, but Raimondas Zutautas equalised within three minutes and in the second half Rangers were distinctly second class.
Inspired by substitute Joel Epalle, Panathinaikos picked Rangers off to march into the last 32 of the UEFA Cup and inflict a fourth consecutive European defeat on the Light Blues.
Mols had waited three years to find the net in the Champions League and when he powered Rangers ahead after 28 minutes it looked as though a good night would ensue.
The Dutchman had netted in the 2-2 draw with Monaco in the final game of the 2000/2001 campaign and perhaps it was written in the script that he should score in what will almost certainly be his last game on this particular stage, given that he will leave Rangers in the summer.
It was an superbly worked goal. Michael Ball took a quick throw in level with the 18-yard box on the left side and Nuno Capucho cleverly played the ball back to him with just the right angle to encourage a cross of quality.
Ball did not disappoint as he swept over an outswinging ball to the front post and Mols met it perfectly to send a header flying into the top left corner.
Alex McLeish leapt for joy in the technical area and he must have felt Rangers were on their way but he was soon cursing his luck as Panatinaikos stunned Ibrox with an equaliser within three minutes.
The Greeks won a throw-in on the left side of the Rangers box and when Markus Munch worked the ball infield for the on-rushing Raimondas Zutautas the danger was clearly imminent.
There was not a Rangers player near the Lithuanian midfielder as he took aim and thundered a low right foot shot into the left corner from some 25 yards.
In an instant the situation had changed significantly and Rangers knew they had some major work to do.
The Light Blues had started fairly well, moving the ball smartly but there was no cutting edge to their play.
Capucho laid off Michael Ball’s cross for Mols in 10 minutes but the striker took too much time and the chance was lost.
And other than a Lovenkrands cross shot which was fumbled by keeper and captain Antonis Nikopolidis but successfully cleared by Munch there was little to trouble the Greeks.
That said, Pana had not looked too threatening in the first half but all of that changed after the break and after little Joel Epalle came on as a substitute for Lucian Sanmartean, who had been booked just before the break for a foul on Ricksen.
Epalle added a new dimension and his cutback in 52 minutes had Rangers in real trouble. The ball broke to Militiadis Sapanis and his driven shot was well blocked by Stefan Klos.
There was another major scare for Rangers in 59 minutes when Epalle charged forward unchallenged and then slipped a great pass to giant striker Michalis Konstantinou who hamered a right foot shot which beat Klos but thumped off the right hand post.
And they were punished three minutes later with another strike from considerable distance which Klos will certainly not be happy about.
Again there was poor covering which allowed Angelos Basinas to take aim and crash a 35-yard shot into the left corner to silence Ibrox.
To make matters worse Zurab Kihizanishvili had to go off in 65 minutes with an injured shoulder after being knocked to the ground by Konstantinou, who then fell on top of him.
Paolo Vanoli was the man to come on and then McLeish sent on Egil Ostenstad for Chris Burke five minutes later as Rangers suddenly had to find an equaliser to keep their European hopes alive.
The Greeks, though, defended stoutly and then they killed Rangers off with a goal on the breakaway which had a suspicion of offside about it although assistant referee Harald Sather had a very good view of it.
Lively Epalle was the man who created it slipping the ball into the path if Konstantinou who raced forward on goal to slam the third past Klos.
It completed an utterly miserable night for Rangers and simply highlighted the problems McLeish has to face right now.
RANGERS: Klos(c); Ross (Duffy 83), Berg, Khizanishvili (Vanoli 65), Ball; Burke (Ostenstad 70), Hughes, Ricksen, Lovenkrands; Mols, Capucho
Subs not used: McGregor, S. Smith, Malcolm, Gibson.
Bookings: Ricksen (82)
PANATHINAIKOS: Nikopolidis; Seitaridis, Morris, Munch; Henriksen, Goumas; Sanmartean (Epalle 45), Basinas, Zutautas, Sapanis (Vlaovic 78), Konstantinou
Subs not used: Kotsolis, Warzycha, Gitas, Konstantinidis, Michaelsen
Bookings: Sanmartean (43), Munch (74).
Ref: Herbert Fandel (Germany)