South African Mallet built a reputation of having a compact rearguard but, under the new regime, Parisse expects new leader Brunel to orchestrate more expansive rugby.
The former Perpignan coach has set out his stall to force Italy into the world's top six during his four-year spell in the Azzurri hot seat, and Parisse believes the players have already seen the difference on the training pitch.
"Over the last four years, we've kicked a lot and been blessed with a very organised, but not aggressive, defence," said Parisse.
"From now on, we want to shift the emphasis more on attack and play in areas of the pitch where we weren't used to playing."
"We will try to keep possession of the ball, to move the ball around to put our opponents in trouble, that's the gameplan that Jacques has asked to produce.
"Brunel's training methods are different from those of Nick [Mallett], their vision of the game is different.
"But it's up to us, and only us, once we're on the pitch, to manage in the best possible way basic scenarios that we've tried over the last week.
"Brunel believes a lot in this squad's potential and we must be convinced that we can reach the goals he's set us.
"Every rugby player enjoys playing with ball in hand and if we want to win we're obliged to take some risks."