Tony Pulis' side now face an uphill task of reaching the next round of the competition as they were outclassed by their technically superior opponents on Thursday
Turkish midfielder Mehmet Topal grabbed his side a vital away goal with brilliant 30-yard effort that flew beyond the hapless Asmir Begovic.
The tall Bosnian goalkeeper had previously preserved his clean sheet when he got down to deny Jonas' shot from close-range as the visitors ultimately ran out comfortable winners.
The Potters made four changes from the side that lost 2-1 to Fulham at the weekend, with Begovic resuming his duties as a 'cup keeper', replacing Thomas Sorensen. Robert Huth, Jermaine Pennant and Rory Delap were the other players to come into the line-up, with Matthew Upson, Glenn Whelan and Kenwyne Jones dropping out respectively.
The away side also made four changes from their 4-0 win over Sporting Gijon at the weekend as Bruno Saltor, Topal, Pablo Piatti and Jonas made the starting line-up. This meant top scorer Roberto Soldado was left with a place on the bench.
The home side came flying out of the traps and could have been ahead within two minutes. Jonathan Walters somehow managed to evade the Los Che rearguard, but could only steer his shot just wide.
Matthew Etherington maintained the early pressure by whipping in a series of crosses that Vicente Guaita and his defenders failed to deal with convincingly.
It took until the quarter-hour mark for the first chance to see a Rory Delap throw-in, but it almost resulted in a break-through. As the ball flew into the area, Walters could only watch on as he narrowly missed a header at the far post.
The Spanish side began to exert their authority though as they monopolised possession and created several openings, with their best chance falling to Jonas.
The tricky striker robbed Pennant of possession before playing a neat one-two with Aritz Aduriz to close in on goal. The angle narrowed but he still unleashed a ferocious strike which Begovic did well to save.
Tony Pulis and his men felt slightly aggrieved minutes later when Peter Crouch went down under the attentions of Bruno, but they could have no complaints about the manner in which they fell behind.
As the ball made it's way to Topal in midfield, little appeared on for the Turk who decided to advance with the ball before going for goal. It proved a wise decision as his strike seared past Begovic to give his side an advantage they probably just about deserved.
Crouch tried to go one better by attempting an audacious bicycle kick from Pennant's right-wing cross. It was slightly reminiscent of his goal against Galatasaray for Liverpool in his Anfield days, but this one rolled just wide.
The second-half proved to be a much more tepid affair as the away side appeared more content to preserve their lead rather than extend it.
The Potters' main threat came through the wing-play of Etherington and Pennant, but they were unable to penetrate Unai Emery's disciplined backline as they stood firm.
Pulis tried to freshen things up by making a double substitution as Ryan Shotton and Cameron Jerome entered the fray, but it was Valencia who came close to striking another blow as Piatti and Sofiane Feghouli combined for the latter to smack a strike against the inside of the post.
The substitutes almost made a telling contribution when they linked up to create the only other real chance of note in the second half. Jerome teed up Shotton to shoot from 20 yards out, but his shot was comfortably dealt with by Guaita.
The final ten minutes proved to be rather fiery as the attention turned to the referee rather than the game. A total of five bookings was racked up as the game filtered out into a rather disappointing end.
The visitors will be more than happy with their night's work, though, as they secured victory against an English team for the first time in nine games to leave them with a great chance of reaching the Europa League last-16 when the two meet again in Spain next Thursday.
Follow the Europa League LIVE on Goal.com:
Commentaries, Stats, Player Ratings and much more,
Visit Goal.com Live Scores!