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.
"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."
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."
