The Potters launched their first European campaign since the 1970s with an away win over Hajduk Split back on August 4 and came through a group containing Besiktas and Dynamo Kiev, winning seven of their 12 games.
It was always an uphill struggle 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 through to a last-16 meeting with PSV Eindhoven.
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. But had Kenwyne Jones made proper contact with either of two golden openings Stoke surely would have taken the lead.
First Rory Delap 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 Ricardo Fuller after he had been well found in space on the edge of the area by Delap.
The game was almost up for the Potters and substitute Roberto 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 Thomas Sorensen did brilliantly to block his shot.