Juncker addressed parliament two days after Greece rejected further austerity measures in exchange for a new bailout.
The Luxembourgish official, who had urged the Greeks to vote 'yes' in Sunday's referendum, told parliament, "the Greek people have spoken and I would like to understand what they said", noting that they had "voted 'no' by a majority on a text that is no longer on the table".
He insisted that the talks would continue, as "not talking means the end of Europe. The Greek government leaving the negotiations was wrong".
Talks between EU leaders were suspended last week after Greek prime minister Alexis Tsipras called a snap referendum.
He added, "the ball is in Greece's court. The Greek government has to explain how they intend to proceed. They need to explain the outcome of the referendum."
An emergency summit is due to take place Tuesday evening in Brussels, to discuss the result of Sunday's vote.
The talks are likely to be tense - on Monday, Greek finance minister Yanis Varoufakis resigned, explaining, "I was made aware of a certain preference by some eurogroup participants, and assorted 'partners', for my absence from its meetings".
Varoufakis has previously stated that Athens would not negotiate with terrorists, and in his speech to parliament Juncker responded by saying, "I do not accept that European institution representatives are called terrorists by the Greek government".
He also warned that the negotiations would be challenging and that a solution would not be found at Tuesday's summit, as, "simple answers are normally wrong answers. There are no simple answers in Europe".
Additionally, he defended European parliament president Martin Schulz, who came under fire after he slammed the 'no' victory.
"It is the right and the duty of the parliament president to speak out on Greece and I am grateful to Martin Schulz for doing so", he told MEPs.
Amid mounting fears of a so-called 'Grexit' - Greece leaving the eurozone - Juncker stressed, "I continue to believe that a Grexit should be avoided, I am against that. Throwing Greece out of the EU or the economic and monetary union is not something we want or should want".
He promised that during the talks, the commission would "show tolerance and restore order", and highlighted that, "we should not forget Greece, but we should not forget the rest of Europe either".