Iceland's joint coach Lars Lagerback says his players have not "started climbing any volcanoes yet" and must be wary of a vastly improved Hungary.
Lagerback watched his side hold Portugal to what is sure to become a famous 1-1 draw in the Nordic country's major tournament debut in Saint-Etienne on Tuesday.
Up next is a clash with Hungary, who defeated the fancied Austria of David Alaba and Marko Arnautovic 2-0 in Bordeaux on the same day.
While some considered Hungary's victory over their highly-rated neighbours to be something of a surprise, Lagerback has been keeping a careful eye on the resurgence of the former powerhouse.
"The Hungary team, they developed through the qualification [campaign] and the play-off [against Norway], how they played some friendlies - I think they have developed their way of playing," he said.
"Even though Austria is a good team, I don't think it was a big surprise. There are such small margins when you come to these championships.
"You can [progress] from a group of death as we did with Sweden once but you can go out also. We're far from that yet.
"We haven't started climbing any volcanoes yet. We have to keep our feet on the ground and do a good job against Hungary, otherwise we will lose that match."
Hungary coach Bernd Storck meanwhile has spent his first year in charge reviving the fortunes of a team that had not qualified for a major tournament since the 1986 World Cup, but carries with it the burden of forever being compared to one of football's greatest teams, the 'Magical Magyars' of the 1950s.
"The great successes of the past are still deeply rooted in the [collective] consciousness, which can be bad for players who already have a lot expected of them," he told DPA, referring to the team that thrashed England 6-3 at Wembley and 7-1 in Budapest, only to lose the 1954 World Cup final unexpectedly to underdogs West Germany.
While the national team is enjoying a minor renaissance, domestically Hungarian football continues to struggle, with the likes of Ferencvaros and Honved no longer regulars on the continental stage.
"The clubs play almost no role internationally," Storck said.
"They usually do not even manage to reach the group stage of the Europa League, let alone the Champions League.
"After the European Championship is qualifying for the World Cup in Russia. Since we want to play a good role again [internationally], the participation here should not be a one-off ... [it is] a huge challenge to permanently bring Hungarian football out of the woodwork."
Iceland, having kept Cristiano Ronaldo quiet at Stade Geoffroy-Guichard, must now be wary of drought-breaker Adam Szalai, who scored for the first time for club or country since December 2014 in the win over Austria.
The Nordic newcomers and their Eastern European opponents meet at Stade Velodrome in Marseille on Saturday, with Group F wide open and one of the two outsiders seeking to take a major step toward the round of 16.