Srebrenica was a Muslim enclave protected by Dutch UN peacekeepers.
On July 11, 1995, it was overrun by Bosnian Serb forces who loaded thousands of men and boys onto trucks, killing about 8,000 of them before throwing their bodies into mass graves.
The plaintiffs, who call themselves the Mothers of Srebrenica, represent some 6,000 survivors of the massacre, and 10 individual widows who lost their husbands in the assault were ordered to pay costs after the decision.
Axel Hagedorn, lawyer for the plaintiffs, told Al Jazeera that they would appeal against the decision and approach the European Court of Human Rights if unsuccessful.
"The mothers will be disappointed ... but this is only the first instance. We will have to see what the appeals court says about this," he said
"If you accept this, then you are saying that only one organisation in the world cannot be judged by an independent court and that is unaccepatable.
"The UN soldiers even helped with the deportation of the men ... so made the mass execution possible."
Hagedorn said that although the case against the Dutch state would continue, the court may decide to put it on hold pending the outcome of the appeal process in the UN matter so as not to split the two issues.
In 2002, the entire Dutch government resigned over an official report that stated its peacekeepers had been sent on an "impossible" mission.
The Serbs brushed aside lightly armed Dutch UN peacekeepers in the "safe area" where thousands of Muslims from surrounding villages had gathered for protection.
The massacre, Europe's worst atrocity since World War II, has been termed genocide by the International Court of Justice, which handles disputes between nations, and the International Criminal Tribunal for the former Yugoslavia, set up by the UN to try war crimes committed during the Balkans conflict.
The remains of thousands of victims have been found in mass graves around Srebrenica since the end of Bosnia's 1992-1995 war.
The UN has also admitted it failed to protect the Muslims of Srebrenica from mass murder, but none of its officials were held responsible.