UK will soon regret voting for Brexit, says the European Commission president
In a speech setting out the future direction of the bloc, Jean-Claude Juncker said the UK's exit would be a "sad and tragic" moment, but it was "not the be all and end all".
Mr Juncker evoked the Queen to describe how Brexit helped to make 2016 an "annus horribilis" for the European project.
But during the annual state of the union address, he insisted the "wind is back in Europe's sails" and countries were knocking on Brussels' door to do trade deals with the EU.
Setting out hopes for closer integration, Mr Juncker announced plans to increase passport-free movement around the EU, expand use of the euro and boost the number of member states.
But the hour-long speech, which ranged over areas as diverse as the quality of fish fingers to plans to create a super-presidency role, Brexit was given a notably short slot near the end.
Mr Juncker said: "This will be a very sad and tragic moment in our history. We will always regret this, and I think that you will regret it as well, soon.
"Nonetheless we have to respect the will of the British people. But we are going to make progress. We will move on because Brexit isn't everything, it's not the future of everything, it's not the be all and end all."
In a letter circulated as he made his speech, Mr Juncker said the past 12 months had been "challenging" for Europe.
He wrote: "2016 was in many ways an 'annus horribilis' for the European project. From the Brexit referendum, to the terrorist attacks, to slow growth and continued high unemployment in several of our member states, to the ongoing migration crisis, Europe was challenged in many ways."
The Queen used the latin term "annus horribilis" - horrible year - in 1992 to describe a torrid 12 months during which the Prince of Wales separated from Diana, the Duke and Duchess of York split up, the Princess Royal divorced and Windsor Castle was badly damage by fire.
Mr Juncker said he wanted use of the euro, membership of the Schengen agreement - which abolishes internal borders, and the banking union set up after the eurozone crisis to become standard.
He insisted it was "high time" that Romania and Bulgaria were included in the passport-free travel area and Croatia should follow soon.
Mr Juncker said the euro is destined to become the common currency of the "entire" European Union.
More countries will become EU members, but Turkey will not become a member for the "foreseeable future", he said.
Mr Juncker said: "My hope is that on 30 March 2019, Europeans will wake up in a union where they know that we are defending their values, where all member states vigorously respect the rule of law, where being a full member of the eurozone, banking union and the Schengen area have become a standard for every member state of the European Union."
Mr Juncker said the EU is open for trade and since last year "partners all over the world are knocking at our door in order to sign trade agreements with us".
He called for more action to end the "scandalous" refugee crisis in Europe and said not all member states were pulling their weight to deal with the problem.
Europe is not a fortress and must be open to asylum seekers, he added.
New proposals on the "opening up of paths of legal migration" will be set out in the coming weeks, but more action will be taken to return people who are in the EU illegally, he said.
Mr Juncker set out proposals to merge his role with the presidency of the European Council, currently held by Donald Tusk, saying it would make EU institutions clearer and more efficient.
Brussels must concentrate on major issues and not "annoy" people with "nit-picking and nitty gritty", he said.
"We need to act on the big things and keep away from the small things, which can be dealt with by the member states," he said.
He said action must be taken to protect consumers in central and eastern Europe who, despite EU rules, were being sold poorer quality products.
"A Slovak deserves to have as much fish in fish fingers as anyone else," he said.
Former Ukip leader Nigel Farage described Mr Juncker's address as "the most open, honest and truly worrying" speech he had heard in his time as an MEP.
"The message is very clear," said Mr Farage. "Brexit has happened, full steam ahead."
Addressing the Parliament in response to Mr Juncker's speech, Mr Farage added: "All I can say is, 'Thank God we're leaving'.
"You have learned nothing from Brexit. If you had given (David) Cameron concessions, particularly on immigration, the Brexit vote - I have to admit - would never, ever have happened.
"And yet the lesson you take is that you are going to centralise and move on to this very worrying, undemocratic union."
Mr Farage said Mr Juncker's vision for the future EU of 27 included a single powerful president, a finance minister with authority to intervene in nation states and "a stronger European army in a militarised EU with a stronger and perhaps more aggressive foreign policy".