"If you want the best out of life you have to be ready when the opportunity comes. That is a fact and these boys were ready today and this opportunity that was put in our hand was huge, it can change their lives," said Hallgrimsson, who combines his role as co-coach alongside Lars Lagerback with his job as a dentist.
Iceland fell behind in the fourth minute in Nice when Wayne Rooney converted a penalty for England but Ragnar Sigurdsson quickly equalised and Joe Hart then allowed a Kolbeinn Sigthorsson shot to dribble into the net for what proved to be the winner in the 18th minute.
"This will probably be a day that we will talk about for the rest of our lives and now we get an even bigger chance in a week," added Hallgrimsson, who will take sole charge of the team after the Euros.
"We are optimistic. Some Icelanders maybe think we are too optimistic, that we don't think we can fail, but we have a game plan."
Iceland's equaliser came just 34 seconds after the restart from Rooney's penalty and Lagerback accepted scoring so quickly was vital.
Lagerback has admitted that he learnt a lot from Roy Hodgson when he worked in Sweden in the 1970s but his stunning triumph also marked the downfall of Hodgson as England manager.
"A part of why I am sitting here now is thanks to Bob Houghton (the Englishman who coached Malmo to the 1979 European Cup final) and Roy Hodgson when they came to Sweden, so I'd like to express my big respect to them," he said.
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