British Prime Minister Theresa May has promised to trigger Article 50 of the EU's governing treaties by the end of March.
Cazeneuve added that Britain must discuss its divorce agreement, including an exit bill that the EU estimates at 60 billion euros, before talks on a future relationship can even begin.
"We must first discuss the conditions in which the exit will take place, and to do it within the time allowed for negotiation, without wasting time," Cazeneuve said after talks in Brussels with Juncker.
Cazeneuve said this should happen "with the aim of ensuring that the interests of the EU are defended and that a state leaving the EU can not benefit from a better regime than that between member states."
Juncker, the former Luxembourg prime minister who heads the executive arm of the EU, gave a similar warning to Britain.
"We agreed on a central point: that the deal that will one day be offered to the United Kingdom should not be a deal as advantageous" as membership, he said.
New European Parliament chief Antonio Tajani meanwhile said MEPs "deserve to be involved in all decisions" about Brexit.
Parliament's Brexit negotiator Guy Verhofstadt has warned the assembly, which has the final vote on any Brexit deal, could veto an arrangement which gives too much away.
British Prime Minister Theresa May has promised to trigger Article 50 of the EU's governing treaties by the end of March, after which negotiators will have two years to thrash out a deal before Brexit happens.
May has said she wants Britain to keep as much access to the EU's single market as possible while limiting immigration from EU countries but Brussels says she cannot pick and choose.
Britain believes the exit bill, which covers budgetary obligations and pension contributions for EU employees, should be closer to 20 billion euros, European sources said.