TUC's Frances O'Grady urges defence of jobs and living standards
Union leaders said the main priority now was to protect jobs.
Most leading unions had campaigned to remain in the EU, although some, including those representing railway workers had backed Brexit.
TUC general secretary Frances O'Grady said: "The British people have made their views clear.
"As the UK prepares to leave the European Union, the first priority now is to protect jobs and defend the living standards of working people.
"The Government must urgently set out a plan to defend UK industry and keep British jobs. That means defending the pound and stimulating the economy.
"Working people must not pay the price for the decision to leave the EU."
Unison union general secretary Dave Prentis said: "We will be working in the coming weeks and months to hold the Leave campaigners to the promises they've made - that there will be more money for the NHS, and that our rights at work will remain intact.
"But this also has to be a time for our country to heal.
"At its best the campaign has enabled genuine debate and discussion in our homes, workplaces and communities about the future of the economy and the kind of country we want to live in.
"At its worst, the campaign has been typified by hatred, vitriol and misinformation that have done a huge disservice to our democracy and values.
"Over the coming weeks and months, all political leaders must think about how to address the issues that people in our communities care most about - falling incomes, insecure jobs, unaffordable housing and the huge challenges facing our public services after more than half a decade of cuts."
Len McCluskey, leader of Unite, said the decision reflected a divided country.
He added: "It is therefore beholden on the party of working people, the Labour party, to stand united to ensure that they deliver on their duty to protect jobs, our public services and living standards from the instability that may follow.
"It is evident that the Conservative party is riven - it is down to Labour to offer unity and calm going forward; anything less will be to let down the people Labour MPs were elected to represent.
"This campaign has uncovered real despair in many of our communities. Too many feel that they have been abandoned by a political class that is not interested in their concerns and has imposed upon them an endless, grotesque austerity programme.
"Little wonder that millions of people expressed their frustrations in the only way that they could, which was to vote for fundamental change in our relationship with the European Union."
GMB general secretary Tim Roache said the country was now in uncharted waters.
"The Government needs to act straight away to secure jobs and keep the economy moving - too many working people are still carrying the can for the last economic crash, they can ill-afford another one, he said.
"What happens next cannot be the preserve of a Government elected with 37% of the vote and potentially a Prime Minister who was never elected at all.
"The British people have spoken, many of them frustrated with business as usual, choosing to leave the EU because of the impacts of the flexible labour market and the pursuit of free trade above all else."