The display was a marked improvement on Zebre's efforts in Europe after defeats to Toulouse and Connacht and was enough to keep them in 11th place in the table with centre Gonzalo Garcia scoring their only try.
But despite avoiding defeat for the second time in six league games this season, Cavinato believes his team are capable of much more.
He said: "I can't help but focus on the chances we didn't take. Even though we played a great game we have to be aware of the fact that we can be competitive against every team if we can keep our precision and limit our errors.
"After Cardiff we maybe thought we were better than we are, we have a lot of growing to do. I want to compliment the players though, with determination and desire they can overcome the difficulties and the countless injuries we're facing at the moment.
"The proof is that the stands were full, the fans in Parma backed us and appreciated our game. We need their support both when we play well as we did against the Scarlets, and in the more difficult periods of the season."