Xherdan Shaqiri's sensational first-half free-kick had the home faithful dreaming of a great escape, only for second half efforts from James McArthur and Patrick van Aanholt seal the Potters' fate ahead of next weekend's curtain closer at Swansea City.
The Baggies remain unbeaten in the five matches since they sacked Alan Pardew, beating Manchester United and Spurs, and registering a 1-1 draw against Liverpool in the process.
On the flip side, however, Crystal Palace securing all three points guarantees them Premier League football next season; a miraculous recovery, given the start to their campaign.
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Scoring goals and an inability to hold on to leads when they did find the net have been two of the most obvious causes for Stoke's relegation, something Lambert acknowledged.
England goalkeeper Jack Butland was left in tears as Stoke City's relegation from the Premier League was confirmed by Saturday's 2-1 dwelling defeat by Crystal Palace. "It didn't happen over one game", Shawcross said.
"It's hard obviously but it's not just about one game".
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Roy Hodgson's side equalised through James McArthur and full-back Patrick van Aanholt capitalised on a Ryan Shawcross mistake to stroke in a 86th minute victor. "For me it would be massive for us to stay up, but it would be bigger for the club".
In the 37 games this season, Stoke won only six, drew 12 and lost 19 matches to eventually fall into the second division. 'You return to July, August, that's when the season begins. I'm gutted for everybody, because it's a brilliant club. Since I came in, the lads have given everything, but we came short. "We've not been good enough all season, and ultimately that's down to the players".
Van Aanholt took to Twitter soon after the win to apologise to the club and fans, and to wish them well next season.
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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!"