The Euro 2016 quarter-finalists, who are the smallest country ever to qualify for the World Cup, will take on the two-time tournament winners at Moscow's Otkrytiye Arena on Saturday.
Hallgrimsson acknowledges that Iceland's World Cup debut is "the biggest game in the country's history" and insists that the team will work as a collective against Argentina and going forward.
"I don't have a magic formula," the 51-year-old told reporters ahead of the Group D encounter. "Everybody has tried everything against Messi and he always manages to score.
"He is one of the best players in the world. We will play against him like everything we do, we'll do it together. We'll help each other and try to do it as a team."
Iceland famously beat England two years ago in France before succumbing to the host nation in the last eight.