Newcastle's relegation from the Premiership was confirmed with a 28-19 defeat at Gloucester.
The Falcons needed maximum points at Kingsholm to have any chance of survival after Leicester's bonus point at Harlequins on Friday.
Gloucester ran in four tries from Jason Woodward, Danny Cipriani, Charlie Sharples and Matt Banahan.
Newcastle's tries came from Michael Young, Sinoti Sinoti and George McGuigan.
Newcastle will stand by director of rugby Dean Richards and "are confident of a return to the Premiership within a year".
The club said: "We remain fully committed to our playing and coaching staff as well as continued investment in our academy, which continues to produce a steady stream of talented local players."
Gloucester dominated the first half and spent long periods in Newcastle territory, turning down a series of kickable penalties before being rewarded with tries from Woodward, Cipriani and Sharples.
Cipriani, in particular, impressed, passing for Woodward's touchdown and then creating space for his own score.
Newcastle only had themselves to blame, playing 20 minutes of the first period with 14 men as first skipper Toby Flood and then second-row Calum Green were sent to the sin-bin.
Newcastle's only two forays into the Gloucester half in the first period resulted in tries for Young - following a powerful break through midfield from Alex Dunbar - and Samoa winger Sinoti off the back of a driving maul as they trailed by nine at the break.
Newcastle dominated the first quarter after the break - helped in part when Lewis Ludlow was yellow-carded - and scored their third try through McGuigan on his debut.
But as the Falcons chased the all-important fourth try and the lead, Banahan intercepted Nemani Nagusa's pass for a length-of-the-field try to all but end Newcastle hopes with a quarter of the game left.
Newcastle will now drop into the Championship after six seasons in the top flight, their place taken by London Irish.
The win for Gloucester confirmed third place in the table and a play-off semi-final against Exeter or Saracens.
Newcastle director of rugby Dean Richards told BBC Radio 5 Live:
"We gave everything, but it was there for the taking. Had we been more accurate it would have been a different game.
"There hasn't been much difference from last year [when they reached the top 4] - the bounce of a ball, a referee's call, it's small differences.
"The games we won last year by a few points we've lost by a few points this year.
"Some [players] will go, some will stay. Some have ambitions to play at a higher level and I completely respect that. That's life unfortunately. We'll resolve those points in the next week."
Gloucester head coach Johan Ackermann:
"We knew what to expect as they were a desperate side, who needed five points. We began well but couldn't convert the pressure and gave away a breakaway try.
"We were never at our best and defensively we switched off in a scrappy game.
"I don't want to be harsh on the boys but as we had already qualified for Europe and the play-offs, there wasn't the challenge for them to excel although I'm tremendously proud of the effort they put in.
Gloucester: Woodward; Sharples, Twelvetrees, Atkinson, Banahan; Cipriani, Braley; Hohneck, Marais, Balmain, Slater, Mostert, Ackermann, Kriel, Morgan (capt).
Replacements: Sherry, Rapava Ruskin, Dreyer, Ludlow, Polledri, Vellacott, Evans, Purdy.
Newcastle: Tait; Kibirige, Dunbar, Williams, Sinoti; Flood (capt), Young; Mulipola, McGuigan, Ah You, Green, Robinson, Chick, Graham, Nagusa.
Replacements: Socino, Lockwood, Davison, Witty, Blamire, Stuart, Swiel, Wacokecoke.
Referee: Tom Foley.
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