Australia logged a 4-1 series triumph after posting just 9-217 and bowling out the tourists for 212 in 49.4 overs.
The game hinged on the dismissal of England all-rounder Ravi Bopara in the 49th over, stumped from the bowling of Clint McKay.
As wickets fell around him, Bopara had coolly made 25 from 44 balls to take the tourists to the brink of victory - but with nine runs needed from as many balls, he fell in cruel circumstances.
The Englishman was stumped when Australian gloveman Matthew Wade fumbled a take - the ball rebounding onto the stumps and replays showed Bopara's feet were in the air by a matter of millimetres when a bail lifted.
His dismissal left England, with one wicket remaining, needing eight runs from the final over, bowled by Shane Watson.
And Watson, who didn't make a run his two outings in the tournament, calmly sealed England's fate by having tailender James Tredwell caught behind on the third-last ball.
England lost their last seven wickets for 58 runs after cruising in their run chase when Joe Root (55 from 86 balls) combined with his captain Alastair Cook and then Eoin Morgan for handy partnerships.
Cook (39 from 62 balls) and Root put on 61 runs for the third wicket, and then Morgan joined Root for a 64-run union.
Morgan continued his stellar series, making 39 from 40 deliveries to take his tournament tally to 282 runs at an average of 56.40 - the highest of any player, ahead of Australian Aaron Finch's 258 runs at 51.60.
But Morgan's dismissal triggered a slump of 4-39 as England required 58 runs from the last 10 overs to win.
Bopara coolly steered the visitors towards their target despite the best efforts of Nathan Coulter-Nile, who claimed his best-ever one-day international figures of 3-34 from 10 overs.
But Bopara's unlucky dismissal summed up England's tour - Australia banked a clean-sweep of the five-Test series before convincingly taking the one-day tournament.
Australian captain Michael Clarke praised the spirit of his players in their comeback win.
"A magnificent performance by the boys, with the ball especially," Clarke said.
"For us to win the game, we had to bowl England out ... and the bowlers executed well."
England captain Cook said his side shouldn't have lost the game.
"We should have got over the line, we got ourselves into a good position but credit to Australia," he said.
"Australia have had a great summer against us and have managed to win the critical times.
"It has been a tough couple of months for us ... we have got a lot to work on."
Australia batsman Finch was named player of the series for his two centuries.