Zanni opened the scoring with a try in the fourth minute but despite conceding two late tries, the 27-year-old believes Treviso are well-placed ahead of struggling Edinburgh's visit to the Stadio Monigo on Saturday.
He said: "After the World Cup us international players wanted to impress in front of our home crowd, I have to say the coaching staff helped us a lot in the reintegration of the squad.
"We've all worked really hard and the result was a fantastic all-round performance.
"We made some mistakes, myself included, especially in defence. We'll analyse them to improve but now we're concentrating on Edinburgh.
"Every team offers different challenges, they come to Treviso knowing that a good team awaits them. For that reason we have to prepare well this week, looking at the three tries we conceded. But I would say we should enjoy the win a little.
"We are better off thinking about ourselves, not the other team. If we can maintain this enthusiasm I don't think we'll have too many problems in the future."
However South African head coach Franco Smith has warned his troops they must not get carried away after the seven-try win over the Dragons.
He added: "A result like the one against the Dragons raises expectations. So the first thing to do is keep our feet on the ground, a year ago we beat Munster and then lost I don't how many in a row.
"Beating Newport would be pointless if we go on to lose against Edinburgh."
63x46.png){kind=logo}