The Juventus midfielder claimed De Canio showed his team a lack of respect after their mauling on Sunday.
Melo said: "De Canio should learn to respect Juve.
"He spoke too much before the game: now he is going home with his mouth shut."
De Canio has now responded by questioning Melo's professionalism.
"I am surprised by the declarations released by Melo at the end of the game," De Canio said.
"I can't understand which part of my interview the Brazilian is referring to, seeing that I only spoke about Juventus-Lecce on Saturday morning and I showed my respect towards Del Neri and the Bianconeri.
"The champions who have been and who are at Juventus would never allow themselves to attack an opponent's Coach without reason above all after having beaten him.
"Felipe Melo goes his own way. When all is told, since his arrival in Italy, he has left a mark above all for his violent behaviour on the pitch and for the behaviour he showed the day after Ciro Ferrara's sacking."