During a question and answer session with young YouTube users, Juncker also denied that he was threatening Britain when he said in a flagship speech this week that it would "regret" Brexit.
His comments came as a senior European Commissioner separately rejected suggestions that Britain would be at the back of the queue when it came to a future trade deal.
"My working hypothesis is that there will be a deal," Juncker said.
Britain and the EU are currently in negotiations on its departure from the bloc on March 29, 2019, following its shock referendum decision to leave last year.
More From This Section
But the EU has refused to discuss a trade pact until there has been progress on the terms of the divorce -- including the bill it says Britain must pay -- raising concerns about whether there will be enough time to reach a deal by Brexit Day.
Former Luxembourg premier Juncker said in his annual State of the Union speech on Wednesday that "we will regret it (Brexit), but you will regret it too".
He said that it was "not a threat" but a "response to an interruption by the far-right" in parliament who cheered when he mentioned Britain leaving the EU.
"I don't want to punish, sanction or make Britain suffer", Juncker said, adding that "I like the English too much".
But he insisted that "the day the UK leaves the EU it will not have the same status in the EU or internationally".
"I've read (news)papers which sometimes refer to some of us saying the UK is the last possible partner with whom we want to negotiate trade. Forget this nonsense," Katainen told a news conference.
"As soon as we know when we can start negotiating about the future arrangement, (trade) negotiations will start then. From our side there is no political priority that we want to keep the UK last in the row," he said.