Bournemouth's five-year stay in the Premier League is over despite claiming a 3-1 win over Everton on Sunday.
The Cherries needed both Watford and Aston Villa to lose to avoid relegation.
Watford were beaten 3-2 by Arsenal but Villa secured a 1-1 draw with West Ham United to finish a point above Eddie Howe's side.
Joshua King scored from the penalty spot after 13 minutes thanks to Richarlison's handball, before Moise Kean tied things up with a simple tap-in.
Dominic Solanke gave Bournemouth a half-time lead with a fine header past Jordan Pickford.
Junior Stanislas sealed the result after his shot squirmed under Pickford to make it 3-1, but it wasn't enough for Bournemouth to survive the drop.
And Howe was understandably disappointed after the final whistle.
"We were excellent today, the frustrating thing when you see us play like that and you wonder where it was throughout the season," Howe said.
"Over a 38-game period we haven't been good enough, I'm not going to sit here and complain about how other teams got their points. When you see how we played today, that is a side that should have got more than 38 points."