A resilient first-half performance from the Italians against Leinster on Saturday once again came to nought as the Irish side triumphed 20-3 at Stadio XXV Aprile.
It had been 3-3 at the break but Ian Madigan touched down after bursting through the defensive line before Luke McGrath crashed over from close-range to give the visitors a hard-fought victory.
The result was Zebre's fifth loss in six games, although they did beat Ulster in Italy two weeks ago, and they sit second-bottom in the GUINNESS PRO12 table.
But Cavinato is adamant his side should have more than just five points and believes the Leinster defeat sums up the injustice of their season so far.
"We are not happy even though the result doesn't tell the whole story of the game," he said. "We faced one of the strongest teams in the world and we deserved to win.
"We did a lot of specific work on our fundamentals this week and I thought our defence and tackling were very effective.
"My staff and I are trying to mould a team where everyone considers it an honour to wear the Zebre shirt and represent this city that even today has supported us.
"A point was within our reach again and our position in the table does not reflect what we have shown on the field in the first phase of the Guinness PRO12."
Click here to see the best images of Saturday's battle in Italy.
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