"No" campaigners celebrate their victory
On Friday, European finance ministers meeting in Brussels put a brave face on the vote against the euro.
The European Economic Commissioner, Pedro Solbes, has said the Danes' decision was "not a great disappointment" and would not hamper the currency system.
Some 53% of Danes voted in Thursday's referendum to keep the krone - a bigger victory for the "no" camp than anticipated.
The euro has remained steady on the financial markets.
A BBC correspondent in Brussels says this may be due to the prospect of further intervention by central banks to prop up the currency, as they did last week.
'Danes to suffer'
The governor of the European Central Bank, Wim Duisenberg, said only Denmark would be hurt by the "no" vote.
"The Danish people have chosen to deprive themselves of benefits in the form of an increase in the rate of growth and the welfare of the economy that would have otherwise taken place and that is already taking place within the euro area," Mr Duisenberg said.
Correspondents say the vote could bring closer the realisation of a "two-speed Europe", in which a core of EU members forge closer political and economic ties than others.
Berlin and Paris are believed to be in favour of a "two-speed Europe" but French Finance Minister Laurent Fabius and his German counterpart, Hans Eichel, said the vote would have no consequences for the euro.
UK and Sweden
Debate about the consequences of Denmark's choice is focusing in particular on the UK and Sweden, two countries also planning to hold referendums on the currency in the future.
But Shadow chancellor Michael Portillo, of the opposition Conservative Party, said there was now less reason for British people to fear isolation if they stayed out of the European single currency.
Swedish Prime Minister, Goran Persson, said the result of the referendum would influence domestic debate in Sweden.
'Worst day'
In Denmark, as jubilant "no" campaigners celebrated victory, the Danish Prime Minister, Poul Nyrup Rasmussen, described the result as a "defeat" for him and his party and warned that Denmark now risked being sidelined within Europe.
Danish Finance Minister Marianne Jelved described her country's rejection of the euro as "the worst day of my political life".
"I fully respect the decision of the people, but I am very sad about it," she said.
The single currency has been adopted by 11 countries in the European Union - but Denmark is the first to allow a popular vote on the issue.
Vote against integration
"It was a very good signal to the political correctness in Denmark to slow down the political integration in Europe, and say that we still want the individual states," she said.
"I'm quite sure that democracy has won."