The Azzurri have failed to win a Test match since beating Fiji 37-31 in Cremona last year and emerged winless from a tour of the South Pacific, including a defeat at the hands of Samoa.
However, Parisse is hoping to avenge that result and build momentum ahead of the clashes with the Wallabies and Springboks.
He told reporters: "For us it was a heavy defeat away to Samoa and it's not going to be necessarily any easier this time.
"They're a strong side, so it's crucial for us to start this Test series off on a positive note before the more difficult challenge of taking on Argentina and South Africa."
Italy are currently five places behind Samoa in the IRB world rankings.