The Swans were dealt their first group stage defeat in the Europa League as their hopes of qualification for the knockout stages go to the last game following a 1-0 home loss to Valencia.
Daniel Parejo's 20th-minute goal proved the difference as Valencia - confirmed as Group A winners following this victory - avenged their 3-0 defeat to Michael Laudrup's side in the opening game of the group in September.
The Swans did have the ball in the back of the net before the break as sub Alvaro Vazquez - on for the injured Wilfried Bony - tapped home after Jonjo Shelvey's volley was parried, but the goal was wrongly ruled out for offside.
The hosts went close in the second half through Vazquez, who saw his effort kept off the line, though Valencia had good chances of their own, most notably through Sofiane Feghouli.
But Laudrup's side couldn't find a way through a resilient Valencia team, who fought hard for their victory.
Defeat means qualification for the final spot in the group goes to the last game.
The Swans, on eight points, head to St Gallen needing just a point while Kuban Krasnodar - on five points - have to beat Valencia and turn around a three-goal difference on the Swans if they wish to qualify.
Further bad news for the Swans were injuries to club-record signing Wilfried Bony, who limped off with a hamstring problem, while Angel Rangel hobbled off late on with an ankle injury.
The Swans make five changes to the starting XI for the Europa League tie with Valencia at the Liberty (8.05pm).
Gerhard Tremmel returns between the sticks in place of Michel Vorm while two changes in defence sees Jordi Amat and Neil Taylor start ahead of Ashley Williams and Ben Davies.
The remaining changes are in midfield as Leon Britton - fully fit following a minor toe injury - returns to captain the side while Jonjo Shelvey - who struck the winner against Fulham last time out - also gets the nod.
Former Valencia winger Pablo Hernandez is included on the Swans bench as he returns from a thigh problem though Garry Monk, Wayne Routledge and Michu all miss out through injury.
SWANS: Gerhard Tremmel, Angel Rangel, Chico Flores, Jordi Amat, Neil Taylor, Leon Britton (capt), Jonjo Shelvey, Alejandro Pozuelo, Nathan Dyer (Pablo Hernandez, 66), Roland Lamah (Jonathan de Guzman, ht), Wilfried Bony (Alvaro Vazquez, 42).
SUBS: Michel Vorm, Dwight Tiendalli, Ashley Williams, Jose Canas.
VALENCIA: Diego Alves, Victor Ruiz, Oriol Romeu, Jonas (Helder Postiga, 77), Sofiane Feghouli (Pablo Piatti, 68), Joao Pereira, Juan Bernat, Andres Guardado, Daniel Parejo, Jeremy Mathieu (capt), Sergio Canales (Javier Fuego, 84).
SUBS: Jaume Domenech, Francisco Alcacer, Ricardo Costa, Miguel Herrero.
The Swans were the first to threaten, with Wilfried Bony's powerful header from a Roland Lamah cross whistling past the post after eight minutes.
The Ivory Coast international went even closer five minutes later as keeper Diego Alves punched Alejandro Pozuelo's corner into the path of Bony, but the striker's header again ended up the wrong side of the post.
Valencia replied via Sergio Canales, who drove low at Gerhard Tremmel, after the visitors did well to create space for themselves.
The Swans were quickly back on the attack and, from the following move, Nathan Dyer rose highest to beat Alves to Neil Taylor's cross, but the ball dropped well wide.
But, on 20 minutes, the hosts found themselves behind.
When Tremmel came off his line to punch a corner clear, the loose was volleyed back by Juan Bernat and took a deflection before falling to the feet of Daniel Parejo, who slotted into the net.
The visitors were comfortable on the ball, and when they found Parejo in space, the midfielder drove low towards goal and Tremmel guided it wide for a corner.
Valencia were utilising their possession usefully, and Jonas fired just over when he found himself in space.
Before the break, the Swans were dealt a blow as Bony was replaced with what appeared to be a hamstring injury. Alvaro Vazquez took his place for the remaining minutes of the half.
And the substitute was straight into the action as he had the ball in the net just three minutes after having come on.
Pozuelo's cross was volleyed towards goal by Jonjo Shelvey, and when Alves parried the effort, Vazquez slid home from two yards only for the linesman to flag to him offside, despite both players appearing to be onside.
HALF-TIME: Swans 0 Valencia 1
Michael Laudrup made a change at the break as Jonathan de Guzman replaced Lamah, which meant Pozuelo moved to the right wing and Dyer switched flanks.
But it was the visitors who made the stronger start as Andres Guardado drove straight at Tremmel before they could - and should - have doubled their lead.
Sofiane Feghouli latched onto a through ball which caught out the Swans defence, and when he looked up as Tremmel rushed out, the midfielder's chip skimmed off the surface and wide.
At the other end, the Swans went close as Angel Rangel nodded a deep de Guzman corner towards goal, but the Valencia defence cleared the danger.
Laudrup made his final change after 66 minutes as Pablo Hernandez came on against his former club in place of Nathan Dyer.
The home crowd were pushing their side on for an equaliser, and they came close when de Guzman's low effort was fumbled by Alves, who then denied Vazquez from the loose.
And the keeper had to be alert to tip wide a Pozuelo cross from the ensuing corner before the visitors raced upfield and wasted a decent counter-attacking opportunity.
But the Swans kept knocking on the door, and Shelvey saw his low drive blocked after some fine link up play by Rangel and Hernandez.
Then, cruelly, the Swans went within inches of levelling as Vazquez saw his shot kept off the line with minutes left to play.
But that was it, and the Swans were dealt their first defeat of the group by a resilient Valencia side.