With Cheltenham beating Doncaster 2-1, Bournemouth needed to win at Carlisle to avoid the drop at the expense of Crewe, who lost 4-1 at home to Oldham.
But Brett Pitman's 68th minute strike was not enough to save the Cherries as they had to settle for a point from a 1-1 draw at Brunton Park.
Manager Kevin Bond said he could not fault his players but felt luck had deserted them just when they needed it most.
"The decisions didn't go our way on the last day of the season, so it's bitterly disappointing and, I must say, really hard to take," he said.
"As well as the lads have done, it doesn't really hide the disappointment. We tried and tried, but it just wasn't to be."