Draghi spoke to the press in Rome on Thursday evening about the visit of European Commission President Ursula von der Leyen and EU Council President Charles Michel to Erdogan on Tuesday.
Von der Leyen was not given a chair at the meeting, but sat somewhat apart on a sofa. Draghi classified this as a "humiliation" of the head of the commission.
"I was very displeased for the humiliation that the President of the European Commission Ursula von der Leyen had to suffer," the former head of the European Central Bank (ECB) said.
"With these dictators, let's call them what they are - who however are needed - one must be honest in expressing one's diverging ideas and views about society," Draghi said.
"But one must also be prepared to cooperate with them in the interest of the country. The right balance is needed," he added.
The choice of the word dictator made many headlines in the Italian media and angered Ankara, with Turkey's Foreign Ministry summoning the Italian ambassador.
"We strongly condemn appointed Italian PM's unacceptable remarks on our elected president, return the impudent remarks," Turkey's Foreign Minister Mevlut Cavusoglu said in a tweet according to state news agency Anadolu.