Sigurdsson admits the draw has been unkind to Lars Lagerback’s men.
But having overcome the odds just to reach the finals, he is confident his tiny nation with a population of just 300,000 can make a big impact.
“We just missed out in the play-offs for the last World Cup, and we had to set ourselves another goal for the Euros, which was to qualify,” said Sigurdsson.
“Of course after seeing our draw, against the Netherlands, Czech Republic and Turkey, some of us considered it impossible.
“But we finished the job off with two games remaining, it was an unbelievable achievement and the feeling that goes with it was indescribable.
“It’s fantastic and we are ready to do it all again in France even if it is a difficult draw we will give it everything.”