Iceland, the smallest country to ever grace a major tournament with just 330,000 inhabitants, secured a last-gasp 2-1 win against Austria thanks to Arnor Ingvi Traustason's stoppage-time effort in Paris.
Their first-ever win at a major tournament sets up a fascinating last-16 clash on Monday in Nice against England - a country approximately 165 times the size of Iceland.
But for Icelandic sports fans, Hallgrimsson revealed the tactics of Roy Hodgson's players will be nothing new.
"Icelanders know everything about English football. We're England football crazy," the joint coach said.
"I don't think we need to analyse them much, that's a benefit.
"There are lots of threats in that team. They are a creative team and there are individual players who can break up the game.
"This is a little bit of a different England team to before. All credit to Roy Hodgson, they are a good passing team with a lot of movement and many creative players."
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Asked what his team would have to do to take their fairytale into the quarter-finals, Hallgrimson said: "I think everyone knows Iceland has to have the perfect game.
"We have to have our best game, we know that.
"Even if Iceland has its best performance ever we can still lose to nations and teams like England, we just have to play our best.
"That's what we have to do."
