Mehmet Topal netted the only goal of the last-32 first-leg tie in the 36th minute at the Britannia Stadium with a 30-yard screamer that gave Asmir Begovic absolutely no chance.
Sofiane Feghouli also hit the post in the second half while Stoke, who have lost their past four Premier League games, were limited to half chances.
Potters boss Tony Pulis described the tie as one of the greatest occasions in the club's history and there was certainly a big difference between the teams in terms of experience, with Valencia playing their 100th game in the Europa League or UEFA Cup compared to Stoke's 15th.
Los Che won the competition in 2004 and are once again the best of the rest in Spain this season, sitting third behind Real Madrid and Barcelona.
The cliche about European teams normally involves asking how they would fare on a wet evening in Stoke, and the hosts were quick to test their opponents, with Jon Walters benefiting from a misplaced header but firing well wide of target.
Vicente Guaita, preferred to Diego Alves in goal because of his prowess at dealing with crosses, coped well with two Matthew Etherington corners but the first Rory Delap long throw caused panic in the Valencia defence and surely would have cost them a goal had Walters managed to get his head on it.
The visitors were treated to jeers and shouts of 'boring' when they finally managed to string some passes together, but Stoke were grateful to keeper Begovic for a great save to deny Jonas after he jinked his way through the defence in the 21st minute.
Valencia's class was beginning to tell and the Stoke defence were called upon to make a number of blocks, while Huth flicked a curling shot from Tino Costa behind.
The Spaniards seemed determined to walk the ball into the net so there was a certain irony that their opening goal after 36 minutes came from a thundering 30-yard shot from Topal that left Begovic pawing at thin air.
Feghouli then fired just wide as Valencia turned the screw but Stoke were almost level moments later when a peach of a cross from Jermaine Pennant was met by Crouch's acrobatic volley that flew just over the crossbar.
Stoke, who did beat Valencia when the sides met in a friendly at the Britannia in 2004, desperately needed something to take with them to the Mestalla next week.
Pennant's crosses looked their most likely creative source and he almost picked out the head of Walters with another gem 11 minutes into the second half.
Pulis had made his first change by that point, sending on Dean Whitehead for the ineffectual Wilson Palacios, while Huth had to be alert to cut out a dangerous low ball from Feghouli at the near post.
Cameron Jerome and Ryan Shotton came on for Crouch and Marc Wilson, but Stoke almost found themselves two behind in the 71st minute when Feghouli again found space down the right.
He jinked his way into a shooting position in the middle of the box and was desperately unlucky to see the ball bounce off the inside of the post and onto Begovic but not find its way into the net.
Stoke continued to probe and Huth stabbed a shot wide from Etherington's corner before Shotton's 25-yard effort deflected off a defender but Guaita recovered just in time.
Leading scorer Soldado, who had reportedly been struggling with illness, came on for the final 13 minutes but the visitors were more than happy to settle for a one-goal victory.