Juncker also told the Spanish daily El País that he wished the Commission had played a more active role in the 2016 British referendum to counteract “lies and fake news”.
Juncker described as “constructive and partly positive” his talks with British Prime Minister Boris Johnson on Monday in Luxembourg.
“I believe that we still have a chance to reach an agreement,” the paper quoted Juncker as saying.
“I don't share the views of those who think that Johnson is playing games with us and with himself,” he said.
Britain's departure from the EU “is a tragic moment for Europe which goes against our sense of history and the spirit of Winston Churchill, who in his day supported a United States of Europe”, he added.
Juncker said he had not been surprised when a majority of Britons in 2016 voted for a departure from the bloc, because they had been told by elites for decades that political union was a “Federalist folly” and that a common market was sufficient.
But it was a regret that the Commission kept out of the referendum campaign when asked to by then-prime minister David Cameron, Juncker said.
“We at the Commission decided not to intervene, at the request of David Cameron, and that was a big mistake,” he said.
Britain is racing toward its October 31 departure without an exit agreement and faces the threat of economic disruption that the government admits could cause food shortages and spark civil unrest.