The three rogue nations refused to ratify the treaty at a meeting of the UN in New York, throwing hopes for new regulation into disarray.
The treaty had required agreement by all 193 UN member states.
But Mr Hague said he was determined to find a resolution. He said: “I am deeply disappointed that the negotiations on an Arms Trade Treaty closed today without consensus.
“After seven years of intensive work, the international community had never had a better chance to agree a global, legally binding treaty that would make the world a safer place.
“The UK has played a leading role and spared no effort to secure a treaty which would be both strong and globally applied, based on consensus.
“We have come very close. It is disappointing that three countries blocked the historic agreement that lay within our reach.”
The Arms Trade Treaty would be the first international, legally binding treaty setting controls on the transfers of weapons, Mr Hague said, and would ban sales of weapons that would be used for genocide or war crimes. Arms brokering would also be regulated, protecting legitimate trade.
He added: “This treaty is too important for us to let it end here. The overwhelming majority of the international community want this Treaty and we are determined to take it forward.”
Other countries also refused to let the treaty die.
Mexico proposed that the UN conference go ahead and adopt the treaty without the support of the three dissenting countries, saying there was no definition of “consensus”. Several countries supported the idea, but the Russian delegation objected.
A Kenyan diplomat, speaking on behalf of a number countries including Britain and the United States, said “the will of the overwhelming majority is clear” and that a letter would be sent to UN secretary general Ban Ki-moon with a draft resolution asking the treaty be brought before the General Assembly for adoption as soon as possible.
Jo Adamson, the British ambassador to the UN Conference on Disarmament, struck a hopeful note. “This is not failure,” she said. “Today is success deferred, and deferred by not very long.”
Ahead of the vote optimism had been growing that the long-debated treaty would become a reality, but concerns remained that Iran and other countries would object.
Both Iran and North Korea are under UN arms embargoes over their nuclear programmes, while the Syrian government is in the third year of a conflict that has escalated to civil war.
Amnesty International said all three countries “have abysmal human rights records - having even used arms against their own citizens”.