But BBC Europe editor, Mark Mardell, says this is a multiple crisis for the EU - a crisis of rule change, of legitimacy and of morale.
In the end, he says, the Lisbon treaty could be declared dead: some parts of it would be implemented without a treaty, others abandoned, others put in a new treaty when Croatia joins the EU in a couple of years time.
Declan Ganley of the anti-treaty lobby group Libertas said: "It is a great day for Irish democracy."
He added: "This is democracy in action... and Europe needs to listen to the voice of the people."
The No campaign was a broad coalition ranging from Libertas to Sinn Fein, the only party in parliament to oppose the treaty.
Gerry Adams, the president of Sinn Fein, said: "People feel secure at the heart of Europe, but they want to ensure there's maximum democratic power."
Correspondents say many voters did not understand the treaty despite a high-profile campaign led by Mr Cowen, which had the support of most of the country's main parties.
Jose Manuel Barroso said the EC respected the vote but had hoped for another outcome
Mr Cowen accused the No camp of "misrepresentation", saying voters had voiced concern about "issues that clearly weren't in the treaty at all", the Irish Times reported.
The treaty, which is designed to help the EU cope with its expansion into eastern Europe, provides for a streamlining of the European Commission, the removal of the national veto in more policy areas, a new president of the European Council and a strengthened foreign affairs post.
The treaty was due to come into force on 1 January 2009.
Fourteen countries out of the 27 have completed ratification so far.
Just over three million Irish voters are registered - in a European Union of 490 million people.
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