More than two-thirds of those who took part in the poll opposed replacing the current method for electing MPs with the alternative vote (AV) system.
Mr Clegg told the BBC the result was "very clear" and promised to "move on".
The No to AV campaign said voters had safeguarded first-past-the-post "for the next generation".
More than 19 million people took part in the referendum on whether to keep first-past-the-post, where voters put a cross next to their preferred candidate, with AV, which sees candidates ranked in order of preference.
These preferences could have been used to decide the outcome in constituencies where no candidate wins more than 50% of votes cast.
The Conservatives backed keeping the existing system, while Mr Clegg's Liberal Democrats urged change and Labour was split on the issue.
Overall turnout for Thursday's referendum was 42%, with 6,152,607 voters backing the proposal and 13,013,123 rejecting it
Mr Clegg said: "I wish I could say this is a photo finish but it isn't and the result is very clear.
"I'm a passionate supporter of electoral reform but we've got to accept this. If, in a democracy, you ask someone a question and get an overwhelming answer, you just have to move on."
He added: "This is a bitter blow for all those people like me who believe in the need for political reform."
Prime Minister David Cameron said the referendum was always going to be a "difficult moment" for the Tory-Lib Dem coalition, but added that the result had been "clear".
He added that the government would continue to deal with the problems facing the UK in a "decisive" way.
Labour leader Ed Miliband, who supported a move to AV, said the public had "delivered a clear verdict which I accept".
But he said elections still had to change in a way which made "people feel more included in our politics".
The AV referendum campaign has been marked by strong words of criticism between the two camps.
In a speech accepting his side's victory, No to AV campaign chairman Matthew Elliott said the result was "clear signal from every part of the country that people want to keep our simple, fair and effective system for electing MPs".
He added: "I personally believe this result will settle the debate about changing our electoral system for the next generation."
However, Katie Ghose, who ran the Yes to Fairer Votes campaign, which called for AV, said: "The referendum hasn't been the debate on issues of democracy that people would have hoped for.
"Too often the debate has been about party politics and the public has been shut out of discussing how we choose our MPs."
She added: "Over five million people voted for change - a tribute to our campaigners."

The 34-year-old South Africa international was sent off in the first half of Saturday's victory over Gloucester for a punch on Nick Wood.
Brits pleaded guilty to the charge at a Rugby Football Union disciplinary hearing on Tuesday.
He will miss matches against Sale, Northampton and London Irish and will be available to play again on 15 March.
The public's overwhelming rejection of a change in the voting system is a "bitter blow", Deputy Prime Minister Nick Clegg has said.
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Saracens hooker Schalk Brits has been banned for three weeks after admitting a charge of striking an opponent.