Celtic made their exit from this competition after a second half of high drama at the Letzi Ground Stadium last night.
The Parkhead side thrice went two behind, but managed to cut the deficit twice with goals from Phil O'Donnell and Henrik Larsson.
But they were eventually undone by a shortage of resources on an evening when six first-team regulars were missing - and by their failure to finish the tie in the first leg.
The surface had been turned into a skid-pan by incessant rain, but that could not explain the early miss by Frederic Chassot from six yards as Celtic's makeshift defence were bedding down with Stephane Mahe and David Hannah forming a new centre-back partnership.
When Celtic began to find a rhythm, orchestrated by their captain, Paul Lambert, the Swiss looked uncomfortable. But the visitors' failure to offer a persistent threat.
Nothing which had occurred could have prepared the crowd for the excitement of the first 15 minutes of the second half.
In the 51st minute, Giorgio Del Signore headed home, and within another five minutes the Swiss were two ahead when Chassot turned Hannah brilliantly before chipping Jonathan Gould.
The applause had hardly subsided when Celtic hit back, as O'Donnell swept home Larsson's cross.
If that raised the hopes of Celtic's fans, they were dashed six minutes later by Shaun Bartlett, who ran clear before pulling the ball wide of Gould and clipping it in from just inside the box.
Larsson responded for Celtic in the 72nd minute with a fierce rightfoot shot from the edge of the area, but it took only another three minutes for the home side to restore their two-goal lead when Sant'Anna's shot took a wicked deflection.
FC Zurich: Pascolo, Hodel, Wiederkeher (Opango 65), Sant'Anna, Bartlett, Lima, Del Signore (Nixon 78), Chassot (Castillo 78), Fischer, Di Jorio, Taroni. Subs Not Used: Tronbini, Huber, Iodice. Booked: Fischer. Goals: Del Signore 51, Chassot 56, Bartlett 61, Sant'Anna 75.
Celtic: Gould (Kerr 64), Mahe, McNamara, Larsson, Brattbakk, O'Donnell, Donnelly, Lambert, Jackson, Hannah, McKinlay. Subs Not Used: McLaughlin, Healy, McBride, Burchill, Crossley, Vaugh. Booked: Donnelly. Goals: O'Donnell 57, Larsson 72.
Referee: L Sundell (Sweden).
