After a night when their familiar defensive frailties were punished ruthlessly by highly proficient opponents, Liverpool will carry no more than limited hope into their second meeting with Celta Vigo in a fortnight's time.
The pity is that the Merseysiders were 60 seconds away from returning home facing a narrow and perhaps retrievable deficit when the roof fell in.
With time almost up, the Spanish team hoisted the ball forward and, as Bjorn Kvarme hesitated, Celta's substitute Vladimir Gudelj sneaked in to stab home his side's third goal, which may prove decisive.
Liverpool's manager, Gerard Houllier, afterwards conceded that his side had been beaten by "a better team".
Although Liverpool led until their resolve weakened in the second period, they were outplayed for long spells. Celta are purposefully direct despite a veneer of flair. By funnelling the ball through central midfield or down the flanks of a curiously narrow pitch, they always threatened to undo a Liverpool defence which still creaks on its hinges despite the experience of its mainstay Steve Staunton.
Houllier's selection, in terms of personnel and tactics, was extremely bold. Having drafted in Kvarme to partner Staunton, the Frenchman pushed Jamie Carragher forward in the hope of nullifying the threat of the highly gifted Alexandre Mostovoi. Carragher did his best but ultimately Mostovoi's deft skills were to settle all the arguments.
Celta grabbed the game by the throat early on. But Liverpool silenced the Balaidos Stadium by taking the lead. In fact Liverpool's first chance of the match after 27 minutes should really have seen them move ahead. Fernando Caceres's dreadful clearance fell sweetly for Michael Owen and there seemed only one logical outcome. But the teenage striker's under-hit shot was comfortably pushed aside by the goalkeeper Richard Dutruel. Even when Robbie Fowler returned the rebound Owen could do no better, missing for a second time as the goal yawned before him. But he soon made amends.
In the 35th minute David Thompson sent a wonderful lofted pass over the Celta defence and the England striker sprinted clear before tempting Dutruel off his line and scoring with a precise low shot.
Strangely, going in front did little to improve Liverpool's fragile sense of self-belief and within five minutes of the start of the second half Celta had deservedly equalised.
After knocking the ball out to the left, Mostovoi found himself well placed to sweep home from 10 yards after the Liverpool defenders had twice spurned opportunities to clear. Worse was to follow.
In the 56th minute a calamitous slip by Vegard Heggem allowed Valeri Karpin the time and space to sweep home a corner delivered, almost inevitably, by Mostovoi.
A booking for Jamie Redknapp means he will miss the second leg at Anfield along with the already suspended Paul Ince and Steve McManaman.
Celta Vigo: Dutruel; Caceres, Vales, Mazinho, Giron; Penev (Gudelj, 83 mins), Sanchez, Djorovic, Makelele; Karpin (Caires, 83), Mostovoi (Echeverria, 88).
Liverpool: James; Kvarme, Staunton, Carragher; Heggem, Redknapp, Thompson (Riedle, 78), Berger (Babb, 85), Bjornebye; Owen, Fowler.
Referee: G Bikas (Greece).