It was always an uphill struggle for the Potters after they lost the home leg last week and, although Kenwyne Jones will look back on two glorious first-half chances, it is Valencia who deservedly go on to a last-16 meeting with PSV Eindhoven.
Boss Tony Pulis had risked the wrath of the thousands of Stoke fans who had travelled out to Spain by leaving the likes of Peter Crouch, Jon Walters, Matthew Etherington and Ryan Shawcross at home.
The visitors were almost behind in only the second minute when Salif Diao conceded a free-kick 22 yards out for a foul on Pablo Piatti and Daniel Parejo crashed his effort against the bar.
Stoke had created very few chances in last week's home leg but they began to find their feet in the cavernous Mestalla, with the front three of Ricardo Fuller, Jones and Cameron Jerome proving a handful for Valencia.
And had Jones made proper contact with either of two golden openings they surely would have taken the lead.
First Rory Delap surprised the hosts by taking a short throw to Fuller, and when he got it back he swung in a perfect cross that Jones should have headed in from only eight yards out.
The striker was culpable again in the 19th minute when a lovely ball from Wilson Palacios picked him out on the edge of the area but he scuffed his shot and Vicente Guaita was able to push it behind.
Somewhat inevitably, Valencia then made Stoke pay as Jonas gave them the lead in the 24th minute, although the goal was not without controversy.
The Potters felt they should have had a free-kick on the edge of the Valencia box when Diego Arismendi tumbled but nothing was given and the hosts broke down the right.
Pablo Hernandez got the better of Danny Collins and ran all the way to the edge of the six-yard box before setting up Jonas for the simplest of finishes.
Stoke responded well and Jones found his shooting boots to test Guaita with a stinging shot from 18 yards that the keeper pushed over the bar, but Valencia gradually re-established their dominance and finished the half much the stronger.
The second half flickered into life with Hernandez shooting off target while Palacios poked a shot wide for Stoke.
Valencia were keeping the FA Cup runners-up at arm's length, although Angel Dealbert needed to pull off a good block to deny Fuller after he had been well found in space on the edge of the area by Delap.
In the 64th minute, Valencia sent on top scorer Roberto Soldado for Jonas, while Pulis made a double substitution, Jermaine Pennant and Ryan Shotton replacing Palacios and Arismendi.
Stoke were struggling to create opportunities, though, and were grateful to Sorensen for preventing a second when he pushed over Parejo's powerful free-kick.
Swedish referee Markus Strombergsson drew ironic cheers from the Stoke fans when he awarded a free-kick on the edge of the area for a foul on Fuller but it was the Valencia supporters who had the last laugh when Pennant slipped and sent his attempted cross straight out of play.
The game was almost up for the Potters and Soldado should have put Valencia out of sight in the 78th minute when he found himself clean through on goal after a mistake by Jonathan Woodgate but Sorensen did brilliantly to block his shot.
Jones headed Pennant's cross wide from a rare Stoke sortie as the game entered injury-time, but there was no way back for Pulis' side, who can nevertheless be proud of their efforts in this competition.