Croatia failed to get out of the group stage in 2002 and 2006, did not make the 2010 World Cup and then went home early from Brazil four years ago.
Those disappointments have merely elevated the status of the Miroslav Blazevic's 1998 team, who were the first Croatian side to feature in a World Cup following the country's independence from Yugoslavia.
Fired up by national pride, they finished second in their group before beating Romania in the round of 16 and then, memorably, upset Germany in the quarter-finals before the adventure ended with defeat by hosts France in the last four.
That 3-0 win over the Germans in Lyon is remembered as the greatest night in Croatian football history although beating Messi's Argentina by the same scoreline has left many experts wondering if a repeat deep run could be on the cards.
"There are a lot of comparisons," Croatia winger Ivan Perisic said on Saturday ahead of training at the team's camp.
"They produced a miracle in France. I was nine years old at the time, watching them and dreaming about being in a similar situation. Now I'm here and we hope that we can come close to what they achieved," he said.
The strength of the current Croat side is in midfield where Dalic can rely on the pairing of Barcelona's Ivan Rakitic and Real Madrid's Luka Modric.
Both scored in the win over Argentina and defender Vedran Corluka believes they are unmatched as a duo.
"Maybe I am a little bit biased but for me they are the best midfield pairing in the tournament and hopefully they can take us a long way," he said.
The 1998 team had plenty of quality in that area too with Zvonimir Boban the main creative force alongside the enigmatic Robert Prosinecki.
Up-front Davor Suker, now president of the Croatian Football Federation, was the tournament's top scorer with six goals.
"They are all legends for the players, they are idols," said Corluka, whose 100th appearance for his country was acknowledged in a brief ceremony on Saturday.
"This is the first time we have passed the group stage in 20 years and hopefully this team will come close to or be able to repeat the same performance," he added.
Croatia did not feature in many pundits' list of favourites for the tournament but Perisic says that was understandable.
"We didn't deserve to be among the favourites after the last 20 years. We went close in Euro 2008 reaching the quarter-finals but now we just need to continue, deal with our final game against Iceland and then the second round."
(Reporting by Simon Evans; Editing by Ian Chadband)
