In the end the decisive moment could have been just after halftime with the score locked at 2-2. The Black Sticks appealed for a penalty corner and the television umpire ruled in the favour of the Netherlands, despite not looking at what New Zealand had appealed for, according to coach Shane McLeod.
"He looked at something else that we didn't ask for," McLeod said afterwards.
The issue provoked a standing argument between Couzins and umpire Nathan Stagno which wasn't resolved to the New Zealander's liking.
From a position of strength and momentum, the Black Sticks suffered another blow when Mink van der Weerden scored to put the Netherlands 3-2 up. Stephen Jenness scored from a penalty corner rebound to give the Kiwis renewed hope but this time the Dutch had the final say.
"The guys are really disappointed," McLeod said before adding that his side's fourth placing in the prestigious tournament would set it up well ahead of next year's Olympic Games in London.
"We gained a lot of confidence and game understanding in playing these types of teams in games of consequence."
Hertzberger scored after five minutes for the Dutch, the ball rebounding in off Pontifex.
Wilson, who plays alongside several of the Dutch players at the Rotterdam club, equalised after a goalmouth scramble.
Teun de Nooijer gave the advantage to the Netherlands before Simon Child slotted home an excellent goal, beating Jacob Stockmann at the near post.
Van der Weerden and Stephen Jenness traded goals and the match looked to be headed for extra-time before de Voogd's intervention. Bakker rubbed salt in New Zealand's wounds when ruling out all hope of a comeback this time.
Couzins felt the New Zealanders had played well in patches, but now it was a matter of stretching out those good passages.
Having lost to Germany on the opening day, the Black Sticks' most convincing performance was in beating Korea 6-1. It was to be their only win of the tournament, a draw with the Netherlands putting them in the top pool where they lost narrowly to Spain and Australia.
"It's a real memory that the guys will hold for a long time," Couzins said of playing in front of a vocal crowd. "The crowd has been fantastic, especially from the Dutch game [on Tuesday] on. I think after the rugby World Cup New Zealanders now get out of their seats and start cheering."
Netherlands 5 (Jeroen Hertzberger, Teun de Nooijer, Mink van der Weerden, Bob de Voogd, Billy Bakker) bt NZ 3 (Nick Wilson, Simon Child, Stephen Jenness). HT 2-2.