The Black Sticks now face Korea in the bronze-medal match at 1:45am on Monday morning (NZT).
Defender Liz Thompson brought up her 150th international cap during the clash.
Head coach Mark Hager said, while the final result was disappointing, it was pleasing to see his side push the best in the world to their limits.
"We were obviously looking for a win to go through to the final, but we knew that was going to be very tough against the Netherlands," he said. "They're ranked number one for a reason.
"It was disappointing to allow them to level it up with that penalty corner, but I thought our defence was good throughout the game and both goalkeepers made some great saves.
"Our focus now is on preparing for Korea in our last game at the tournament and making sure we put our best performance out there to come home with the bronze medal."
The Dutch held greater possession and created more scoring opportunities in the first half, but the Black Sticks' defence was strong, as it has been throughout the whole tournament.
New Zealand struck first in the 34th minute, when Charlton put a precision ball into the circle and Pearce deflected past the goalkeeper's feet.
Netherlands equalised midway through the fourth quarter from a penalty corner, which Caia van Maasakker sent into the roof of the net.
Neither side could find a winning goal over the final 10 minutes and Kiwi keeper Grace O'Hanlon made some outstanding saves in the dying minutes to take the game to a deciding shoot-out.
By making the top four at the World League Semi Final, the Black Sticks have qualified for the 2018 Hockey World Cup in London.
New Zealand also qualified for the FIH Women's World League Final in Auckland from November 17-26, although they were already an automatic inclusion as the host nation.
The Netherlands, China and Korea will join New Zealand at the World League Final, following results in Brussels, while the top four finishers at the World League Semi Final in Johannesburg will also book a spot.
New Zealand 1 (Kirsten Pearce) Netherlands 1: (Caia van Maasakker)
Netherlands won shoot-out 5-4
Halftime: 0-0