Playing in their fourth World Cup, New Zealand were again denied a maiden victory when Lieke Martens' 33rd minute curling strike from outside the area sailed past the outstretched arms of Erin Nayler.
"It was just one bit of brilliance from a player that we knew was capable of that, that made the difference," New Zealand coach Tony Readings told reporters.
"We challenged ourselves as a team that we had another couple of gears to go up. We played OK in the first half but OK isn't good enough in the World Cup.
"When we do up the ante and play to the pace we are capable of we can out-perform teams in this tournament.
"It's a good lesson for us."
Considered the tournament dark horse by many, New Zealand stormed through qualifying, outscoring opponents 30-0, but failed to test Dutch keeper Loes Geurts despite enjoying the better of the play.
Scoring goals has become a major problem for the Ferns, who have now failed to find the back of net in their last four contests - against Spain, United States, Japan and the Netherlands.
"We need to make our opportunities count because when you get to these tournaments it's not just about putting in a good performance it's about putting in a good performance and win games or take points," Readings added.
The win moved the Netherlands to the top of Group A alongside Canada who opened the tournament with a 1-0 win over China.
Next up for the Dutch are China while New Zealand will face Canada.
"We're very happy we could start this way," said Netherlands coach Roger Reijners. "Everyone was very excited to be here but we know what we want."
