To reach the last 16 on their World Cup debut, Iceland must beat the Croatians and hope Nigeria fail to beat Argentina. Even then, qualification could be decided by goal difference.
"We are optimistic about everything. If it’s the Eurovision song contest we always think we’re going to win it, even though we never do. It’s the same here, optimism is in our genes," Hallgrimsson told a news conference on Monday.
"We think we’re going to win all the games, and even if we lose we think we’re going to win the next one."
Iceland's titanic task could be eased if Croatia coach Zlatko Dalic sticks to his promise of rotating his team to keep his squad fresh, his side having sealed their place in the next round by beating Nigeria 2-0 and Argentina 3-0.
Croatia need a point to guarantee top spot, although they could still finish first even if they lose to Iceland.
Dalic is expected to leave out six players on yellow cards who risk suspension including Mario Mandzukic and Ivan Rakitic, while 32-year-old captain Luka Modric and Liverpool defender Dejan Lovren could also be in line for a rest.
Lovren has revealed that the reserve players have twice beaten the first team in Croatia practice matches at their training base.
Hallgrimsson also believes his opponents decision to unleash a batch of fresh players eager to prove themselves could work against his Iceland side.
"It's actually a disadvantage for us, it's strange to say it but now we have players coming in who are still at the highest level, all motivated players who want to punch themselves into their first team," he said.
"So we have to approach it in the same way, it doesn’t matter if they change one player or 10."
Iceland beat Croatia while qualifying for the World Cup and finished ahead of them to top their group, something captain Aron Gunnarsson said would further boost his side's hopes even though the odds are stacked against them reaching the knockout rounds.
His side should also be able to count on the support of locals at the Rostov Arena, since three Iceland players play for FC Rostov.
"We know we're up against the wall but beating Croatia before gives us belief," said the midfielder.
"Having three players at Rostov will be good for our support and that makes a difference, as we saw when we beat Croatia at home. Hopefully the fans will be on our side tomorrow and we can play well and do our job, that's the only thing that matters."
(Reporting by Richard Martin; Editing by Tony Lawrence and Pritha Sarkar)
