The 71-year-old says nothing but a win will do ahead of meeting league leaders Juventus at the weekend and believes his team currently occupy a false position in Serie A
The Rosanero have collected an impressive 11 points from their previous five games, a run of form which has lifted the club out of the relegation zone to 17th in the Serie A standings.
However, Guiseppe Sannino's men travel to Turin knowing their opponents need only a point to secure the league championship.
Speaking to Radio Kiss Kiss, Zamparini said: "We are desperate for the win and we'll be going to Turin to win. We need the points and we have to try cause an upset.
"We will not go there hoping to spoil Juventus's party, but with the intentions of having our own party."
Asked about his club's chances of avoiding the drop, the 71-year-old was optimistic.
"Ourselves and Genoa are much stronger than the teams ahead of us," he added. "But things can still go wrong."