It ranked alongside their 1-0 loss to the part-timers of the United States at the 1950 World Cup and sent Iceland, appearing at their first major tournament, into a glamour quarter-final with hosts France.

Hodgson said England needed a new coach.

Hodgson’s four-year contract was due to expire at the end of the tournament.

Hodgson says “I would have loved to stay on another two years, however I’m pragmatic and know that we’re in the results business.”

He adds his contract “was always up after the Euros, so now is the time for someone else to oversee the progress of this young, hungry and extremely talented group of players. They have been fantastic and they have done everything that has been asked of them.”

Hodgson left the press conference room immediately after reading out his statement and a Football Association press officer said that he would not be performing any other media interviews.

Hodgson said that his assistants, Ray Lewington and former Manchester United captain Gary Neville, would also be standing aside.

Ironically, Hodgson’s fate was sealed by his former protege Lars Lagerback – Iceland’s joint coach alongside Heimir Hallgrimsson – who began his coaching career under the Englishman’s tutelage in Sweden in the late 1970s.

Monday’s result at the Stade de Nice, against a team from a country with a population of just 330,000 and with no previous tournament experience, brought a miserable end to Hodgson’s four-year tenure.

Appointed manager following Capello’s abrupt resignation in May 2012, he led England to a creditable quarter-final finish at Euro 2012, where they lost on penalties to eventual finalists Italy.

But the 2014 World Cup in Brazil was a disaster, as England crashed out after just two matches in their worst tournament performance since the 1958 World Cup.

“I’m extremely disappointed of course about tonight’s result and ultimately our exit from the competition,” Hodgson said.

“We haven’t progressed as far as I thought we were capable of, and that’s obviously not acceptable.

“I’m actually proud of the work my coaching staff and I have achieved over our time at the helm of England.

“The transition from the squad whose average age was 30 to now being the youngest in the tournament is both remarkable and exciting for the future of English football.”

He added: “I’m sorry it’s had to end this way with another exit from the tournament.

“These things happen. All I can do is wish everybody all the very best and hope that you will still be able to see an England team in a final of a major tournament fairly soon.

“We’ve been unable to deliver. Thank you very much.”

As expected, Hodgson made six changes to his starting XI at a muggy Stade de Nice, which included a recall for Raheem Sterling.

The Manchester City forward was criticised for some insipid group-stage displays, but he made an excellent start, racing onto Daniel Sturridge’s fine pass and drawing a foul from Iceland goalkeeper Hannes Halldorsson.

Rooney planted the penalty into the bottom-left corner to crown his 115th England appearance – which tied David Beckham’s record for an outfield player – with a 53rd international goal.

Remarkably, his side’s lead was to last only 34 seconds.

Hodgson had warned of the dangers of Aron Gunnarsson’s long throw-ins prior to the game, but from the Iceland captain’s right-wing missile, Kari Arnason headed the ball on and Sigurdsson charged in behind a dosing Kyle Walker to volley home from close range.

It drew a roar from the blue-shirted fans in the Iceland end and after Dele Alli and Harry Kane had fired narrowly over for England, they were screaming with disbelief in the 18th minute.

Gylfi Sigurdsson and Jon Dadi Bodvarsson worked the ball to Sigthorsson and with England’s defenders standing off, the Nantes striker rolled a shot goal-wards that Hart could only palm into his bottom-left corner.

Having also allowed a Gareth Bale free-kick to squirm past him in the 2-1 win over Wales, it was the City goalkeeper’s second major blunder of the tournament.

Kane threatened to provide an immediate riposte with a stinging volley that was brilliantly palmed over by Halldorsson, but in the main Hodgson’s men were reduced to long-range potshots.

Hodgson made two attacking changes – Jack Wilshere replacing Eric Dier at half-time, Jamie Vardy taking Sterling’s place on the hour – but despite their firepower, there was no craft whatsoever to England’s approach play.

Had Ragnar Sigurdsson’s overhead bicycle kick not flown straight at Hart early in the second half, meanwhile, England would have had a mountain to climb.

But Sigthorsson’s goal was to prove enough, with Alli hooking over and Kane heading straight at Halldorsson before the final whistle brought England’s players to their knees and sent the Iceland bench tearing onto the pitch in celebration.