After the 26-16 loss in Parma last weekend, tries from Michele Campagnaro and Edoardo Gori helped Treviso to a 17-15 victory in the return fixture, moving them off the bottom of the GUINNESS PRO12 table at the expense of their fierce rivals.
Quintin Geldenhuys' score kept Zebre in it before Brendon Leonard's late try brought them within two points, but it was not enough as Jayden Hayward's boot proved to be the difference.
And an angry Cavinato knew his side had only themselves to blame for the defeat.
"We played like chickens, making big blunders with the two tries," he said. "I told my team to play around the meeting places with penetrations and changes of angle.
"But instead we were looking to move the ball sideways and I don't know why. It was a big mistake from my team.
"Anyone that says I don't have respect for Treviso is wrong. I played here and worked for years and I have a great respect for them.
"Now we are the last and behind Treviso, but we will work very hard to try and get to the sixth or seventh place, where we should be."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland