The Sicilians secured a spot in the final after a shock 2-1 defeat of newly crowned Serie A champions AC Milan in Sicily, completing a 4-3 aggregate victory.
"Now we're going to the final and we'll beat Inter 3-1," he said to AFP.
"This team is more mature than the one that blew qualification for the Champions League last season."
The Palermo president also admitted that he was so nervous that he couldn't watch his team's shock victory over AC Milan.
"I didn't watch the game as I normally do and I went for a drive around the city, looking at many lovely and suggestive places," he confided.
"At half-time I discovered it was 0-0. I arrived at the stadium in the 92nd minute with the score at 2-0 and I thought I would go and wave to the fans but as soon as I stepped foot on the pitch, Milan scored, so I went back to my office."
Despite his excitement in winning a place in the Coppa Italia final, Zamparini revealed that reaching the top flight with Palermo seven years ago was actually a finer moment.
"This joy cannot be compared with that of 2004 when we were promoted to Serie A," he said.
And although he's predicted a win, it's clear that his nerves continue.
"I will only celebrate after we've won the Italian Cup. I was afraid because we were playing against an expert side and the fact that we always mess up in the crunch games," he concluded.