England's calamitous World Cup campaign suffered its final indignity as a 15-run defeat to Bangladesh sent them crashing out of the tournament amid controversy in Adelaide.

Eoin Morgan's men were consigned to a group-stage exit, alongside the likes of the United Arab Emirates and Afghanistan, after failing to chase down 275 for seven.

It was an achievable target just large enough to tease the nerves out of a chastened England team as they were bowled out for 260 in 48.3 overs.

England had some reason to feel aggrieved, however, after Sussex's Chris Jordan was contentiously adjudged run out by third umpire Simon Fry after Jos Buttler had kick-started a rousing comeback with 65 from 52 balls.

Coach Peter Moores said: "It is hard to get round it - I thought 275 was chaseable and we didn't do it. It is hard to analyse anything at the moment. I have been in the dressing room and everybody has their heads down.

"They are all gutted. We got off to a reasonable start - most people thought spin would be the problem on that pitch but we got bowled out by the seamers. At some point we have to look at one-day cricket full stop and where we go with it.

"Every day you look at if you could have got it right. Now, you feel hollow inside and hugely disappointed. You're not think a lot about if you did things right. Any analysis will be done later.

"It's not my decision if I'm given time. I'm here to try to make a difference. You can't look too far ahead. We should have won that game and we should take that on the chin.

"I understand why people would think I'm not he right man, but it's a bigger picture than that. We haven't played good ODI cricket for a while. We brought what we thought were an exciting group of players, young. There's work to do. The players aren't bad players, but we haven't played well enough.

"We prepared well. We covered the right stuff, but we haven't played well. We have to take that."

Jordan had reached beyond the crease but TV umpire Simon Fry felt his bat had bounced up into the air as Shakib Al Hasan's throw hit the stumps.

Moores cut an irate figure on the boundary and he did not take his seat again as he watched his side fall agonisingly short.

James Anderson was left head bowed as the last man out, bowled by Rubel Hossain, who had started England's panic with two wickets in an over midway through a pursuit gripped by twists and turns.

Ian Bell had looked to pace the pursuit with 63 from 82 balls, but slashed behind before skipper Eoin Morgan then followed when he pulled straight to Shakib on the square-leg rope for a duck - his fifth in nine innings.

It capped a miserable first tour in permanent charge for Morgan, who was handed the captaincy after Alastair Cook was axed for a lean run during the pre-Christmas tour of Sri Lanka.

Mahmudullah's maiden one-day international century proved critical after Anderson had given England a dream start with two wickets in his first two overs.

The 29-year-old right-hander, who had never scored more than 82 in his previous 113 ODIs, calmly restored the sort of calm that England lacked when they suffered their own mid-innings wobble.

England appeared resigned to their fate when Joe Root edged behind and they were 163 for six. Buttler was left with no recognised batsman to partner and a required rate spiralling past nine runs an over.

The 24-year-old revealed none of the nerves that had racked those before him, however, as he instead displayed the power and invention that has marked him as England's most eye-catching talent.

He brought his half-century up from 41 balls and, with Chris Woakes looking similarly assured, they stole the momentum away in a 75-run stand from 61 balls.

But the game took another twist when Buttler edged Taksin Ahmed behind with 38 still needed and then Jordan was controversially given out.

There was yet more drama as Woakes was dropped in the deep by Tamim Iqbal and Stuart Broad crashed a six.

But Rubel finished the game off as he bowled Broad and then yorked Anderson to spark Bangladeshi celebrations as they reached the World Cup knockout stage for the first time.

The defeat will leave Moores with plenty of serious questions to answer in the coming days, when England will prepare for their final group game against Afghanistan in Sydney on Friday with nothing to play for.

England reached the Tri-Series final just five weeks ago but since then a gulf in class between them and the full-member nations has been powerfully illustrated in heavy defeats to Australia, New Zealand and Sri Lanka.

Even after those defeats England were expected to overcome Bangladesh and they made changes for the first time at the World Cup as Alex Hales and Jordan were drafted in for the must-win game.

England had stuck with the same team through their opening four games but a return of just one win against lowly Scotland forced a reshuffle that left out-of-form Gary Ballance and Steven Finn on the sidelines.

Morgan's decision to bowl after winning the toss was immediately rewarded when Anderson removed openers Imrul Kayes and Tamim to catches in the slip cordon in his first two overs.

Imrul edged the fourth ball of the day to Jordan at third slip before Tamim offered a regulation chance to Joe Root. In between Tamim had already survived a Jordan dropped catch diving to his left.

Anderson celebrated both wickets with fist pumps, to typify England's early aggressive intent, and he might have even had Mahmudullah before he got going when the right-hander inside-edged just past his stumps.

England's change bowlers failed to maintain the early pressure, however, and Mahmudullah was able to ease his side's early discomfort in an 86-run stand alongside Soumya Sarkar.

Moeen Ali removed the dangerous Shakib, caught by Root at slip, and Bangladesh were 99 for four.

Morgan reinserted Broad as he sensed an opening and the diminutive Mushfiqur Rahim targeted early on with some short-pitched bowling. The skipper withstood the challenge and with Mahmudullah shaped the Tigers' innings in a 141-stand that was careful for far longer than it was carefree.

Mushfiqur did most of the risk-taking, as he rattled along at just over a run-a-ball, but Mahmudullah was rewarded for his graft with his first century after 114 ODIs.

It came from 131 balls, with seven fours and a pair of sixes, but a Woakes direct-hit from short third-man prevented him from going on for more.