Speaking on Wednesday, Arlene Foster said the talks failed due to disagreements with Sinn Féin about legislation for the Irish language.
But Ms Villiers insisted the success of failure of negotiations "ultimately depends on Northern Ireland's leaders and in particular its two largest parties, the DUP and Sinn Fein".
She urged the parties to "reflect" and think about the future.
But she said Sinn Fein's demand for an Irish Language Act to enshrine the status of Irish was not "fair and balanced" and did not respect "the unionist and British identity" of Northern Ireland's Protestants.
The British and Irish prime ministers met political leaders in Belfast on Monday, as the two main parties in Northern Ireland edged closer to unlocking a political stalemate that has left the region of 1.8 million people without a government for more than a year.
Mr Murphy told Radio Ulster that "good faith" that has existed during the negotiations "evaporated" with the DUP move.
Civil servants have been running Northern Ireland's rudderless public services since the last DUP/Sinn Fein-led coalition imploded last January in a row over a botched green energy scheme.
"At that time we advised the DUP leadership that the deal should be closed before those opposed to it could unpick what we had achieved", said the Sinn Fein leader.
That rift subsequently widened to take in more long-standing disputes over language, social issues and the legacy of the Troubles.
Britain's Northern Ireland Secretary, Karen Bradley, said in the absence of a Northern Ireland administration "other challenging decisions will have to be taken by the United Kingdom government".
"We had a way forward on all the issues", said Michelle O'Neill, the party's leader in Northern Ireland.
As it stands Mrs Bradley is under a legal obligation to call another snap election in Northern Ireland but few observers see the merit in such an option, given it would likely return the same political make-up and not resolve any of the outstanding issues.
"They have now collapsed this process". The DUP used a petition of concern to veto these bills, arguing that such legislation did not command enough cross-community support under the complex rules governing power-sharing in Northern Ireland.
Dublin TD McDonald said there would be no quotas on Irish speakers for jobs, nor would the language be forced on anyone.