This weekend they welcome a Dragons team still smarting from a 60-3 home defeat to Glasgow Warriors, and who will be without international pair Toby Faletau and Andrew Coombs who are away with Wales.
But despite that, Troiani warned that Zebre have been in the same position before where they have gone into a game with confidence only to fall short.
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 might 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."
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