Rafael Benítez regularly pleads for time; on this evidence, he will need it.
Olympiakos dismissed the Merseysiders with ease, making light of the late loss of their full-back Anastasios Pantos for a pair of bookings. The Greeks, inspired by Rivaldo's presence subjected Liverpool to a torrid night. Liverpool improved marginally after the interval, but they were still helpless as Leroklis Stoltidis thumped a second-half header against the bar.
The substitute Stylianos Venetedis should have scored in the dying moments, wriggling through a poorly organised offside trap only to drag a shot across goal. There was something alarmingly lacklustre about Liverpool's display throughout, their zip still elusive when necessity demanded a more urgent approach late on.
This was always likely to prove a daunting task, as Liverpool's away form under Benítez has been too insipid for comfort. The raucous din greeting them here did little for their nerves, though even the fluorescence of their shirts failed to guide them in possession as swathes of acrid flare smoke rolled across the turf.
Even Xabi Alonso, normally so imperious, was forced into mediocrity by the early onslaught, Liverpool gasping for breath amid a series of rampant Greek attacks. Only when the home players opted to crumple to the turf under the vaguest hint of a challenge - something they did shamelessly and regularly - did Liverpool find brief respite, though it was through a set-piece that Olympiakos scored.
Inevitably, it was Rivaldo who prompted the panic. The 32-year-old wears No5 these days with the general consensus that he is half the player he was since, as Brazil's No10, he helped inspire them to the World Cup two years ago.
Yet from set-plays his class still shines through. There was a reverse flick at the kick-off to set the tone, a blistering volley from distance which burst beyond Jerzy Dudek but wide, before he ambled, bandy-legged, up for a succession of free-kicks around Liverpool's penalty area.
From the fourth - Stephen Warnock having apparently obstructed Dimitrios Mavrogenidis - Rivaldo's centre flicked off Milan Baros, barely 10 yards from the Brazilian, to veer awkwardly into the area. Dudek and his defenders were too static to repel the threat and Stoltidis, leaping around the penalty spot, flicked the loose ball home. Benítez, who watched his side concede twice from set-pieces at Manchester United last week, was apoplectic on the bench.
In truth, Liverpool should have drawn encouragement of sorts to trail so narrowly by the break. Ioannis Okkas and Mavrogenidis cut through their left flank at will with Stoltidis, freed by Okkas early on, forcing Dudek to touch a shot on to his near post.
The goalkeeper's horribly sliced clearance nine minutes before the interval was centred first time by the excellent Grigorios Georgatos with Giovanni unable to convert from point-blank range. Then Pantelis Kafes should have converted the midfielder's corner moments later.
The locals might have considered there to be a makeshift air about Liverpool's line-up, with Harry Kewell on the bench due, apparently, to a thigh injury and Djibril Cissé dropped, though that did not excuse the shoddiness of their display.
So ineffective and downright sluggish had Liverpool been that the Australian, niggling injury or not, appeared belatedly for the second half at Warnock's expense. Thereafter Benítez's side steadily found width, if not necessarily poise.
Steve Finnan had opportunities to deliver from the flank but found ever more elaborate ways either to over-hit or scuff his crosses. There was more threat when Baros's typical run across the box culminated in a flick inside for Kewell to gather, only for a linesman's flag to choke his attempt.
The decision was marginal, even though Antonios Nikopolidis blocked the shot. The goalkeeper helped steer his country to European Championship triumph back in July; Greek football has never enjoyed days as heady as these.