Cesare Prandelli's side failed to make it out of Group D after Tuesday's 1-0 loss to Uruguay saw them finish third - the second consecutive World Cup in which Italy have failed to reach the last 16.
Prandelli offered his resignation following back-to-back defeats for Italy but De Rossi - absent from the final group game due to a leg injury - appeared to take aim at controversial compatriot Mario Balotelli, who recently posted a picture via Twitter showcasing his Panini collection with his sticker in every slot.
"There were certainly components that affected the result, like the heat or the refereeing, but we must not cling to these things," said De Rossi.
"We must forget about all this quickly. Actually, I take that back: we should remember well what went wrong and begin again with real men.
"We need real men, not Panini stickers or characters. These are of no use to the Nazionale."
Meanwhile, captain Gianluigi Buffon felt it was time to reflect after a disastrous campaign in Brazil.
"As a group and as a nation, it is a very sad day," he said.
"It is a day of failure and is something that saddens us very much.
"(The loss) should make us all think and let us take a good examination of our conscience."
