Prop Castrogiovanni and fly-half Bocchino clashed during a game of touch rugby at Otago Stadium ahead of Sunday's 'winner-takes-all' clash with Ireland.
However Parisse believes the flare-up is evidence Italy are ready to produce something special, rather than a sign that the pressure is getting to his squad.
"At the captain's run, as always, we had a game of touch," said Parisse.
"We always play forwards against backs and I don't know why but until now, the forwards always won.
"So today, before the game, I told the backs 'try to beat us at least today'.
"Between Castro and Bocchino, there was a little discussion, because Castro took the ball and Bocchino wanted to stop him and so hit him in the face with his hand.
"Castro, as everybody knows, is not the kind of guy who lets things go easily, but Castro and Bocchino apologised in front of everybody at the end of the session.
"The positive thing is that we are all tense and generally when we are tense like this we play very well.
"Congratulations also to Bocchino. Not everybody would have faced Castro like that!"
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