The supposedly faded Brazilian, a World Cup winner in 2002, created the only goal, by Ieroklis Stoltidis midway through the first half. He also delivered the corner from which Ioannis Okkas headed against the bar with 16 minutes remaining. Even after Anastasios Pantos was sent off for a second bookable offence after 83 minutes, Liverpool could not turn their belated pressure into a first scoring chance.
Liverpool's campaign continues next month with back-to-back matches against Deportivo La Coruña. The Spaniards' Riazor stadium can be a soundtrap of Galician aggression, but Rafael Benitez's players should at least be able to hear themselves think, which may have been hard at times amid the cacophonous din of Olympiacos' refurbished home.
For the 22-year-old Stephen Warnock, who was given his first start in Europe because of doubts over Harry Kewell's fitness, it was a baptism of smoke. Acrid, red fumes at that, from the flares lit by Olympiacos' supporters. They had barely cleared before an attack down the left, where Warnock was practically in direct opposition to Rivaldo, signposted the attacking threat posed by last season's Greek runners-up.
In the fifth minute, a probing pass by Stoltidis played Okkas into the danger area to the left of Jerzy Dudek's goal. Rounding the Liverpool captain, Sami Hyypia, with ominous ease, the striker tried to beat Dudek low by his near post, only to direct the ball against the upright.
Rivaldo, one of Pele's more distinguished successors in Brazil's No 10 shirt, returned to Europe from his homeland during the summer for one last pay day. Nowadays he wears No 5, but if Liverpool hoped he might be only half the player he was, the 32-year-old former Milan and Barcelona midfielder soon produced evidence to the contrary.
After 17 minutes, Rivaldo's set-piece prowess led to Olympiacos seizing the lead. His free-kick picked out Stoltidis, who outjumped Hyypia to head powerfully inside the left-hand post from 10 yards. As if to prove he is no mere place-kicker, Rivaldo then received a short pass from his compatriot and ex-Nou Camp colleague, Giovanni, and let fly with a first-time shot from 25 yards. The ball was a white blur as it flashed inches wide, doubtless to Dudek's relief as he scrambled across.
Benitez, on the touchline, wore the look of a holiday-maker who arrives to find a building site where his villa should be. Olympiacos' touch and movement would not have surprised him, yet the way in which Liverpool were embarrassed in the air was definitely not in the brochure. Pantelis Kafes did it again just before half-time, from a corner taken by Grigorios Georgatos, but his free header flew narrowly over the bar.
Warnock, having been booked for scything down Dimitrius Mavrogenidis and had scant opportunity to impress in a mediocre collective display, gave way to Kewell after the break. .
A long-range effort by John Arne Riise, was Liverpool's first shot worthy of the description - 10 minutes into the second half. Kewell's introduction did give them a modicum of impetus, although they were back-tracking desperately after Rivaldo executed the deftest of nutmegs on Hyypia before being coralled by the yellow-shirted posse.