The Dutch water polosters finished second in their group at the Olympic qualifying tournament (OKT) in Trieste.
The team of national coach Arno Havenga was too strong for France in his last group match on Thursday with 15-6, but that was not enough to keep Italy from the first place.
As expected, the Italian women had no trouble with Slovakia (26-4) two hours after the Orange game and thus secured group win.
As the Netherlands and Italy tied in their mutual game on Wednesday (7-7), the result in the game against France is decisive.
Since Italy had won 19-6 against the French team, a Dutch victory with at least fourteen goals difference was needed on Thursday to stay ahead of Italy.
The Orange had an excellent start and led 8-2 after the first period.
After that, the game of the Netherlands became more difficult, so that not enough was scored to stay ahead of Italy.
Dagmar Genee and Simone van de Kraats were top scorers on the Dutch side with four goals each.
Final ranking group A OCT
1. Italy 3-7 (52-17)
2. Netherlands 3-7 (44-15)
3. France 3-3 (29-43)
4. Slovakia 3-0 (15-65)
Orange will meet Kazakhstan or Israel in quarterfinals
In the quarter-finals, the Netherlands will take on Kazakhstan or Israel on Friday.
Those two countries did not score a point in the other group and will play against each other later on Thursday.
The winner will meet Orange.
There are two tickets to be distributed in Trieste for next summer's Olympic Games in Tokyo.
That means that the decision falls in the semi-finals.
Normally, the Dutch will have to earn Olympic qualification on Saturday in the semi-final battle against Greece.
The Greek women beat competitor Hungary (8-5) on Thursday, making them the winner of the other group.