Newport Gwent Dragons have won just one of their last six contests: 23-14 at home to Treviso earlier this month and have not won away from home in the PRO12 since a visit to Edinburgh in March 2012.
The Welshmen have lost only one of their last five fixtures against Italian opponents but Troiani is confident of ruining that sequence.
He said: "We have to win the Dragons game, but it's not the first time that we have had that, we could or maybe should have beaten Cardiff, the same with Connacht, and we weren't good enough.
"On Sunday we have to show a lot of determination because I'm convinced we can win.
"Marco Bortolami will be back which could help. He brings some stability to the team.
"We want Sunday to be our reference point. We have to work on our game management in defence and attack.
"In Belfast it was good and I'm sure on Sunday Marco will give us that guidance that has been missing."
The Italian side will have to cope without experienced flanker Mauro Bergamasco however, after he was called up by national coach Jacques Brunel.
However, Troiani insists he is happy to see Bergamasco join the likes of Giovanbattista Venditti and Luciano Orquera in the international reckoning.
He added: "We are delighted to see our players called up to the national team. If Mauro and others are called up, it's a reward for our work. If they are called up it means there is a reason for the squad. It's one of the objectives of the squad."
Meanwhile, Newport Gwent Dragons coach Darren Edwards has backed his experienced players by selecting Adam Hughes, Ashley Smith, Wayne Evans and Phil Price to all start against Zebre.
Price, who will make his 14th start this season for the regional side said: "We know what they (Zebre) are about and we played them at the start of the season, they have improved as the season has gone on, especially up front.
"So we have to think of ourselves and make sure that we put a good performance in.
"I have come back with a more positive attitude to regain my place and try to keep it. I have worked hard this week. We have pulled tighter as a unit and we are all looking forward to the Zebre game and putting in a good performance."
At Stadio XXV Aprile , 3.05pm local time (2.05pm UK & Ireland)
Referee: Leo colgan (IRFU, 10th competition game)
Assistant Referees: Andrea Spadoni, Simone Boaretto (both FIR)
Citing Commissioner: Roberto Carra (FIR)
TMO: Alan Falzone (FIR)
Delayed coverage on Sportitalia