"We are aware that discontent with the functioning of the EU as it is today is manifest in parts of our societies. We take this very seriously and are determined to make the EU work better for all our citizens," the foreign ministers said.
But with Eurosceptic parties calling for their own referendums on EU membership, the rhetoric must be matched by swift action. For Italians, one of the main complaints is about economic austerity set by Brussels and the idea that they must bow to stronger countries, such as Germany. A survey last month found 48 per cent of Italians would vote to leave if given a chance.
Pier Carlo Padoan, Italy's Finance Minister, said that "business as usual" was no longer an option for EU leaders and bureaucrats. There had to be more emphasis on economic growth and job creation, particularly in Italy where youth unemployment has topped 40 per cent. "The unthinkable is happening," the minister told Corriere della Sera. "A double reaction to Brexit is under way, one financial, one political ... I am more worried about the political one. There is a cocktail of factors that can lead to various outcomes, including a further push to disintegration."
La Repubblica summed up the feelings of many. "Europe without Great Britain is a mutilated Europe. A great nation has left. There is now an exit route from Europe. The ban on leaving has vanished."
Populists and Eurosceptics across the Continent were now eager to sink the "damaged ship" of the EU, the paper added.
Jean-Marc Ayrault, France's Foreign Minister, said the EU must change to contain the threat of a Brexit contagion. "The main thing is that we must make Europe more concrete and effective for people. There is still too much unemployment," he said.
Who wants to exit next?
Austria
Norbert Hofer, Third president of Austria's lower house of parliament; former presidential candidate, Freedom Party of Austria. Hofer supports the idea that Austria must act independently of the European Union. Hofer tweeted, "#Brexit What an exciting night. The EU must break new ground if you want to survive". He lost a cliffhanger presidential election in May by 0.3 per cent .
Belgium
Tom Van Grieken, Party councillor, party board, national chairman, Vlaams Belang. Van Grieken is the 29-year-old leader of Belgium's far-right Flemish nationalist party, Vlaams Belang, which advocates splitting Belgium into Dutch and French-speaking nations.
Denmark
Kristian Thulesen Dahl, Leader, Danish People's Party. Congratulating the British in a Facebook post, Thulesen Dahl said: "The EU has taken too much power from the states and is now paying the price". The DPP opposes the EU.
France
Marine Le Pen, President of the National Front; member of the European Parliament. Le Pen celebrated Brexit, urging France to vote for a referendum on the country's membership with the European Union. She is surging in the polls ahead of the 2017 presidential election.
Germany
Frauke Petry, Chairwoman, Alternative for Germany. "The time is ripe for a New Europe," Petry tweeted. Her party is poised to win big in parliamentary elections next year.
Hungary
Viktor Orban, Prime Minister of Hungary, national conservative Fidesz party. Orban shut Hungary to refugees last year, exacerbating the crisis.
Italy
Beppe Grillo, Founder, Italian Five Star Movement. Grillo, a comedian-turned-politician, has electrified voters fed up with their country's old-style politicians. Five Star politicians were elected mayors of Rome and Turin.
Netherlands
Geert Wilders, Founder, Dutch Party for Freedom. Wilders tweeted: "Hurrah for the British! Now it is our turn." Wilders says Britain is paving the way for the liberation of European countries.
- Telegraph Group Ltd, Washington Post