Gylfi Sigurdsson bagged a first-half brace as Iceland made it three wins from three matches in Euro 2016 Group A qualifying in Reykjavik on Monday.
It was Iceland's first win against the Dutch as the Nordic nation - yet to concede a goal in qualifying - moved level on nine points with Czech Republic.
Hallgrimsson, who is working alongside Lars Lagerback, as he prepares to succeed the Swede ahead of the 2018 World Cup qualifying campaign, lauded his defenders on the back of a third consecutive clean sheet.
"This is a world-class team we have beaten. First and foremost, it was a really solid team performance," Hallgrimsson said post-game.
"I think our defensive display was the key to winning. They knew what to do and stayed focused. We had planned how to defend against them and it worked."
Sigurdsson produced another memorable performance for Iceland, converting a 10th-minute penalty before doubling the hosts lead three minutes shy of the half-time break.
Speaking post-match, the Swansea City player credited Hallgrimsson's game plan for the historic victory.
"A fantastic result. We knew we were going to be chasing the game a lot and that Holland would be keeping possession more than us, but we worked hard and our plan worked perfectly: defend and hit them on the counterattack," he said.
"We knew how good they are – especially with [Arjen] Robben and [Robin] van Persie up front – but the way the coaches set us up worked perfectly."
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