He told the BBC: "What has happened today means that it is no longer possible to have a referendum on the Lisbon Treaty.
"We have campaigned for that referendum for many years, we believe passionately that there should have been a referendum so that the British people could be consulted.
"But now that the treaty is going to become European law and is going to enter into force, that means that a referendum can no longer prevent the creation of the President of the European Council, the loss of British national veto.
"These things will already have happened and a referendum cannot unwind them or prevent them - and that means that our campaign for a referendum on the Lisbon Treaty therefore comes to an end today. We think that is a bad day for democracy."
Mr Hague said the Conservatives would "not let people forget whose fault that was," adding: "Gordon Brown and the Labour Party promised people a referendum at the last election and people have never been consulted in a referendum or a general election."
Foreign Secretary David Miliband said: "So much for David Cameron's cast-iron guarantee to hold a referendum on the Lisbon Treaty.
"But he is still not being honest with people. The fact is you can't simply opt out of treaty obligations because to do so you need the agreement of the 26 other member states.
"David Cameron's position on Europe is false and dangerous. He is willing to risk Britain's standing and the rights of British people because he is still not prepared to stand up to the right of his own party."
Labour insists the Lisbon Treaty is not the same as the defunct constitutional treaty, on which it had promised voters a say.
Liberal Democrat foreign affairs spokesman Edward Davey said earlier that if Mr Cameron could not make his position on Europe clear "he is not fit for government".
UK Independence Party leader Nigel Farage said: "Mr Hague says it is 'no longer possible' to have a referendum.
"Well, to me and millions of others it is apparent that it is no longer possible to trust the Tory party or David Cameron when they make promises about Europe."
Eurosceptic Conservative MP Bill Cash said he had written to Mr Cameron urging him to "reconsider" his decision not to hold a referendum, saying the Tory leader had been "badly advised".
Sources say there is likely to be an EU summit next week to discuss who will fill the posts of President of the European Council and High Representative for Foreign Affairs, which will be created when the treaty comes into force.
Former UK Prime Minister Tony Blair is widely seen as a candidate for president.
Despite his insistence that he is "not available" to take the job, David Miliband is being considered as a possible High Representative - in effect Europe's first foreign minister, sources have told the BBC.
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