Hodgson made the announcement straight after the game, where his side failed to beat the representatives of a country with a population of 323,000 that only has 100 professional players.
Hodgson made the following comments:
"My 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 I have asked of them".
Hodgson went on: "I`d like to thank all the support staff, players, the FA and of course the fans. It`s been a fantastic four years and it`s one I`ll look back on with pride."
And finished saying: "I`m sorry it`s had to end this way with another exit from a tournament but 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 very soon. We`ve been unable to deliver"
England, who had failed to impress at Euro 2016, started the match brightly with Sterling winning a penalty which was converted by Rooney. But Iceland struck straight back with Sigurdsson firing home to level the tie. And just before the 20th minute Sigthorsson fired in a fairly weak shot that Kane got a hand to, but couldn`t stop.
England looked desperately for an equaliser for the remainder of the match but looked toothless up against a well-drilled Iceland defence.
Iceland now face France in the quarter-finals on Sunday.
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