Gasperini lost his first two games in charge of the Rosaneri, but after thrashing Chievo 4-1 and drawing at his former club Genoa, he now feels he can lead the club back into a position where they can challenge for a place in Europe.
"A new season starts for us now," he said. "Our immediate goal is to beat Torino, then in the future, I want to lead this team on to the heels of the top clubs."
Despite a difficult start to life in Palermo, the former Genoa coach said he always felt there was enough potential within the side to justify his decision to accept the challenge.
"Despite losing to Atalanta and Pescara, I could see an identity," he told the Gazzetta dello Sport newspaper.
"Furthermore, the lads always had belief and the reason we are doing well now is that they are working well."
Midfielder Massimo Donati does not believe the corner has been turned yet, though, and he says tomorrow's match is a pivotal one.
"Our league position is not good so if we win a game like this one, we can move up the table and catch up with Torino themselves," he said.
"We are on the right track, but in addition to playing well, we need the results because you don't go anywhere without those."
The key to Palermo's upsurge in form has been the recent performances of Fabrizio Miccoli.
"It wouldn't be a bad idea to clone him," said Gasperini. "He may not be how he was when he was 20, but he is certainly not old. He is always positive."
Angelo Ogbonna will be out to stop Miccoli after recovering from the injury which forced him to miss Italy's 3-1 win over Denmark in midweek.
Kamil Glik could partner him after scoring Poland's equaliser in a 1-1 draw with England on Wednesday.