One win from their last three Group A qualifiers will ensure a place at Euro 2016 in France for the Nordic nation.
"Some might think we have been a little naive but always it has always been our target and aim to qualify Iceland.
"In the past maybe it would have seemed strange to think we could come and beat a strong football power like Holland," Hallgrimsson said after Thursday’s 1-0 win over the Dutch.
"But going so close in the playoffs against Croatia gave the players the belief we can achieve it,” he added, referring to Iceland reaching the 2014 World Cup qualification playoffs where Croatia beat them 2-0 on aggregate over two legs. “We could smell going to Brazil. It gave everyone the belief that has never been there before.”
Iceland's victory in Amsterdam completed a double over the Netherlands and kept Iceland two points ahead of the Czech Republic at the top of the standings.
A home win on Sunday against Kazakhstan, who have lost six of their seven qualifiers, will take Iceland to 21 points and confirm a top-two finish and a trip to France next year.
“Let’s hope we can do it. We are not there that yet but in a very good position in the group.”
Iceland must still play second-bottom Latvia at home in October and will complete the campaign away to Turkey. Iceland’s newspapers on Friday encouraged supporters to begin booking their trips to next year's finals.
In Amsterdam on Thursday, 3,000 travelling fans, about one percent of the north Atlantic island nation’s population, were roaring their players to victory.
(Editing by Ken Ferris)
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