Seven points from three games under returning coach Giuseppe Sannino have brought Palermo within two points of safety in Serie A.
The Rosanero would have claimed nine, though, had goalkeeper Stefano Sorrentino not gifted Bologna an equaliser with his blunder in last weekend's 1-1 draw at the Renzo Barbera.
Zamparini is now concerned that confidence has dropped at a critical time and, with Catania pushing hard for a Europa League place, he hopes his players do not freeze under pressure.
He told the Corriere dello Sport: "We have everything to be scared of in the derby as Catania go into it as favourites.
"Palermo have more desire to win than they do, but we also have more fear.
"I hope this game isn't decided by another unfortunate incident like what happened with Sorrentino.
"But Catania and Palermo are playing the same type of football at the moment and so one-off incidents could prove decisive.
"It will be a very difficult game but we will give it our best shot."
Palermo are missing talismanic striker Fabrizio Miccoli through injury but Sannino is boosted by the long-awaited return from injury of Abel Hernandez.
The Uruguayan forward, who made his first appearance since October as a substitute against Bologna, is raring to go at the Stadio Angelo Massimino.
"The first few months after the injury were very hard and I got a bit depressed," he said. "But now I feel stronger than I was before.
"It's a very important game and I want to play a part. I've not got 90 minutes in my legs so it's up to the coach to decide how to use me."
Bragging rights aside, Catania are still chasing their all-time points record in the top flight after failing to beat Chievo last weekend.
Victory over Palermo would see Rolando Maran's men reach 50 points and better last season's haul of 48 and the Elefanti coach has no desire to take pity on Palermo tomorrow.
"They will be determined to save themselves but we must continue to dream too," he said. "We have to improve our league position and try to beat our points record."
The injured trio of Fabio Sciacca, Adrian Ricchiuti and Pietro Terracciano are unlikely to feature.