Bailey heads the opening goal for Charlton at The Valley
Norwich joined Charlton in League One after crashing to a 4-2 defeat.
A win and Barnsley losing at Plymouth would have kept the Canaries up but they were three down within 30 minutes.
Nick Bailey headed Charlton ahead, Deon Burton tapped in a rebound and diverted home Bailey's cross, before Alan Lee nodded one back late in stoppage time.
Burton completed his hat-trick, Sammy Clingan fired a free-kick for 4-2, but Norwich slipped into the third league tier for the first time since 1960.
These two sides were playing in the top flight only four years ago.
Norwich were top of the table for much of the Premier League's first season in 1992-93 and beat Bayern Munich away the following term.
They would have been hopeful of a dramatic escape against a Charlton side already relegated and condemned to the third tier for the the first time since 1981, who had won only four of 30 games under Phil Parkinson.
Sure enough Barnsley conceded an early goal, but the large Norwich contingent were still celebrating that when Bailey planted a simple header into the net after Sam beat Jason Shackell to the byline.
Sam was soon in the action again when his shot was only parried by David Marshall and Burton was on hand to apply the finish.
Norwich would still have harboured hopes of a recovery given Charlton's unfortunate record of squandering two-goal leads twice in their last three games.
But even the most optimistic follower of the Canaries would have been contemplating trips to Carlisle and Hartlepool with news of a Barnsley equaliser.
That was swiftly followed by Burton's slight touch to make it 3-0 and it prompted chants of "You're not fit to wear the shirt" by the demoralised visiting contingent.
It threatened to be a repeat of four years ago when Norwich needed to win on the final day at Fulham to stay in the Premier League and duly lost 6-0.
With two seconds remaining of a lengthy spell of first-half injury time, Lee bundled in from a corner, Norwich's first effort on target, but six minutes into the second half Charlton got a fourth.
Sam weaved through once more and squared for Burton, who was able to bury the chance despite being prostrate on the turf.
After Clingan's free-kick, Simon Lappin thought he had made it 4-3 from another set piece, but referee Russell Booth decided it had been taken too quickly and compounded the frustration by brandishing a yellow card.
Barnsley's victory meant the result was academic in any case, and Norwich and Charlton must regroup together in League One next term.
Charlton manager Phil Parkinson:
"If I'm not here next season I'll walk away with my head held high.
"The club has had a lot of instability. If the board, or any new owners, want to start again I think that will be a big risk."
Norwich boss Bryan Gunn told BBC Radio Norfolk:
"Over the course of 90 minutes, I feel very let down.
"I didn't expect that level of performance from the players on such an important day, performances like that are the reason we've been relegated.
"I've told the players to go away and look at themselves in the mirror, the ones that want to be at this club next season will hopefully come and knock on my door, look me in the eye and say they want to play in League One next season.
"I want the job even more now because it's my fault we've been relegated, I'm big enough as a person to take that on my shoulders, hopefully I'll be given the chance to move the club forward."
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