The Italian outfit ended a run of 11 successive European defeats when they overcame Ospreys 23-20 last weekend but still lie 11th in the GUINNESS PRO12 table with just two wins to their name.
Zanni was part of the powerful Treviso pack that caused Ospreys numerous problems at the Stadio Monigo and eventually forced a winning penalty try with less than ten minutes remaining.
And while the 30-year-old flanker pinpointed the squad's hard work as a key component of their success, he was quick to remind them that there is still more work to be done.
"It is not just me or others but the whole team that has worked hard to pull off this victory," Zanni told la tribuna di Treviso.
"We really wanted to win because we wanted to cancel out our poor performance in Paris [against Racing Metro] and have success in front of a big crowd.
"So, there is a satisfaction on the part of all of us. Congratulations to all but we must progress from here.
"In Glasgow and Cardiff we played a good game but to win, there is a difference. I am convinced we are going in the right direction - a month ago to score a try would have been very difficult to imagine."
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