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!"
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.