Burnley were relegated from the Premier League on Sunday, the final day of the 2021/22 season.
The Clarets had to better the result of relegation rivals Leeds to extend their six-season stay in English football's top flight.
But Burnley lost 2-1 at home to Newcastle while Leeds won 2-1 away to Brentford.
"It's raw, we've got a group of players who are gutted," Burnley interim manager Mike Jackson told the BBC.
"I don't think there is any other word to say about that. The effort they've put in since we came in has been brilliant.
"Today we've come out on the wrong side of chasing the game. We had some really good chances but couldnt take them."
He added: "There is a lot of emotion in it. I'm gutted for everyone involved but proud as well as I couldn't have asked any more from them."
Burnley kicked-off outside the relegation zone, albeit they were only above Leeds on goal difference.
But they fell behind at Turf Moor to Callum Wilson's 20th-minute penalty following Nathan Collins's needless handball.
Wilson then doubled Newcastle's lead on the hour when he headed in from a cross by Allan Saint-Maximin.
Burnley, who sacked long-serving manager Sean Dyche with eight games to go, pulled a goal back as Maxwel Cornet fired in a volley after his first effort had been parried by Newcastle goalkeeper Martin Dubravka.
But that was as good as it got for the Clarets, with Leeds winning away to west London club Brentford thanks to Raphina's second-half penalty and a goal in stoppage time from Jack Harrison.
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