Xherdan Shaqiri had given them hope when he scored his eighth goal of the season with a first-half free kick. His attempt went in the top right corner of the net, beating Crystal Palace keeper Wayne Hennessey in the 43rd minute.
With Palace not at their sharpest in a nervy opening half, it took the quality of Shaqiri to break the deadlock as he began a promising move with a fine cross-field ball, then tempted Ruben Loftus-Cheek into a clumsy challenge 23 metres out.
Stoke goalkeeper Jack Butland was in tears at the final whistle and City fans were just as emotional as the realisation of their team's relegation sank in.
Two teams between West Brom, Huddersfield, Southampton and Swansea will join Stoke City in the Championship next season in the coming weeks.
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"Any joy I feel is measured by looking at the faces of the Stoke players who gave everything, but I don't think they could have done anymore, they came up against a team who weren't willing to lie down, who put in a top, top performance".
Stoke at 19th position, have only recorded 30 points in 37 games and have negative goal difference of 34.
Match victor van Aanholt apologized for scoring on Twitter: "Normally I like to celebrate when I score but I'd like to apologise to Stoke City and their fans, I wish my goal didn't relegate you, but you'll be back soon!"
As a Stoke fan and a season ticket holder I am heart broken with the result, but this tweet has really touched me.
Normally I like to celebrate when I score but I'd like to apologise to Stoke City and their fans, I wish my goal didn't relegate you, but you'll be back soon!
"It is so disappointing and hard to take but this is an incredible Club and one that I truly believe will be back".