"My wish is that a 'Grexit' should be avoided," Juncker told the European Parliament in Strasbourg just hours before an emergency summit in Brussels on the crisis.
"There are those in the EU who openly or otherwise campaign for Greece to exit from the eurozone. My life tells me the simplistic answers are the wrong solutions," he said.
Finance ministers from the 19-nation eurozone meet in Brussels at 1100 GMT to review the situation before their leaders gather at 1600 GMT amid mounting concern that Greece could crash out of the single currency area and possibly even the European Union.
A Greek referendum Sunday saw 61 percent reject more austerity terms demanded by creditors in exchange for fresh funds desperately needed to keep the country afloat.
Juncker, in his first public comments since Sunday's vote, said the EU would continue to work to re-open negotiations with Athens but told Greek Prime Minister Alexis Tsipras it was time to get to the point, to spell out clearly what Sunday's vote means.
"Now it is time for those with common sense and reason and a degree of emotion to negotiate. The Greek delegation walked out of the negotiations. That was wrong; that was a serious error; you don't walk out of negotiations," he said.
At the same, Juncker warned that a "solution is not going to appear overnight".
"If we were going to come up with a solution today, that would be an overly simplistic solution," he said.
"What we are going to do today is to talk to each other, to understand each other, to show tolerance and to restore order to the situation."