One shouted at him: 'It's a British issue'.
To heckling from Ukip MEPs, Juncker added: "Then the time will come when you regret your decision".
Michel Barnier said any attempt by Britain to gain a competitive edge through the use of what is termed "dumping" would jeopardize hopes the country has for a smooth and orderly withdrawal from the EU.
Germany's BDI industry body wants the European Union to agree a customs union with Britain to limit the impact on trade after it leaves the European Union, its managing director told the Frankfurter Allgemeine Zeitung newspaper. If you made a decision to jettison, leave behind, the common agreements and rules then you have to accept that things can not remain what they are ...
Addressing the European Parliament, Mr Juncker was cheered by Eurosceptic MEPs as he noted the UK's departure was due on 29 March 2019.
But he warned that the border between Northern Ireland and the Republic could be a major roadblock to sealing a deal.
He also defended an European Union proposal for the bloc to continue to regulate trade in the British province of Northern Ireland after Brexit, should no other ways emerge to avoid a hard border between that territory and the country of Ireland.
He said it "translates faithfully" the agreement reached between Theresa May and the European Union in December.
And the former Luxembourg PM warned London the European Union institutions and member states stood squarely in support of Ireland on the issue. For us, this is not an Irish issue.
Goldman Sachs and UBS said last week they were starting to transfer some bankers to Frankfurt in preparation for the U.K.'s exit from the EU.
The European Parliament's Brexit co-ordinator Guy Verhofstadt also called for more details from Ms May.
He said: "There was this Mansion House speech by Mrs May, but it was mainly repeating the red lines that we know already".
"As the clock ticks down with one year to go, it is now time to translate speeches into treaties, to turn commitments into agreements, broad suggestions and wishes on the future relationship into specific workable conditions", he said in what can be seen as a rebuke to the speech of British Prime Minister Theresa May earlier in the month.