In his state of the union address to Parliament on Wednesday, Juncker said that while he "deeply regretted" the UK's decision to quit the EU, predictions that it would sound the death knell for the bloc were untrue.
"The EU is not at risk as a result of this," said the Commission President.
He also insisted that the UK could not expect to retain "unlimited access to the single market without accepting free movement of labour."
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He declared, "There can be no à la carte access to the single market."
Juncker, speaking ahead of an informal EU leaders' summit on Friday, also said that while he "respects" the UK vote, Britain should trigger article 50 "as soon as possible so that we can start the steps necessary for British withdrawal."
He added that despite what some may see as a hardline approach, he wanted the EU to retain "friendly" relations with the UK, albeit with a "new shape."
He also told MEPs that the trade implications of the EU referendum could not be overlooked, saying, "The EU has trade agreements with 140 countries and is in a good position to enter into new deals."
Despite Brexit, he made robust defence of the EU but conceded that the next 12 months were "crucial" in "delivering a better Europe."
His wide-ranging state of the union speech comes on the day the Commission decided to set up a task force for the preparation and conduct of the negotiations with the UK under article 50 of the Lisbon treaty.
This follows the appointment on 27 July of former Commissioner Michel Barnier as chief negotiator in charge of the talks and of the related Task Force. The Commission has also appointed Sabine Weyand, currently Deputy Director-General in the Commission's trade department (DG TRADE), as deputy chief negotiator .
Meanwhile, ALDE group Chair Guy Verhofstadt has come attack under for over his appointment as Parliament's Brexit negotiator.
Ukip MEP Nigel Farage told a lively state of the union debate the Belgian was an "EU nationalist" whose choice amounted to a "declaration of war on any sensible Brexit talks."
Farage called the former Belgian Prime Minister a "high priest fanatic" who should not have been selected for the role.
He added, "The European Parliament's choice of Verhofstadt, as the Parliament's chief divorce lawyer following the Brexit vote in the UK places a dangerous fanatic in charge of the process. He is anti-British to the core, and not a man with whom we can have a grown up conversation."
Verhofstadt hit back, saying that Farage and others in the Leave camp had offered a "false sense of security" to voters.
He argued that rather than being a "liability", British exiting the EU could be seen an "opportunity" for the EU to "reinvent" Europe.
"Britain wants to make Brexit a success and that's fair enough, but our job is to make the EU a success. There's no question of revenge or punishing the UK and we need to stop this collective depression on both sides of the channel."