"As children growing up, we never really looked at our national team. We looked at Brazil and Spain but now the youngsters are watching us and I hope they're looking up to us," Sigurdsson told reporters in France.
"People kept on telling me that Iceland would never play in a major tournament but I always believed it would happen and it's great we're there."
The 26-year-old, who also had spells at Tottenham Hotspur and Reading, added that Iceland should look to Leicester City's title-winning season to seek inspiration.
"You know, it has been a crazy season but every team is sitting and watching Leicester and thinking, 'How is that possible?' Maybe it will be similar with Iceland," Sigurdsson added.
"If you have belief, good players and confidence then anything is possible."
Austria and Hungary are the other teams in the group.
(Reporting by Ian Rodricks in Bengaluru; Editing by John O'Brien)
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