The former Australia mentor was named Sydney's seventh coach in eight seasons on Wednesday, replacing Ian Crook, who stepped down from the position earlier this month.
Farina was dumped after three seasons with Roar in October 2009 after being caught drink-driving on his way to training, the second time he'd been picked up over the the legal alcohol limit.
"I think he's determined to come back and have another go," Pignata said on Wednesday.
"So he's determined to come in and make amends, definitely."
Pignata admitted the appointment had received a mixed reaction but implored fans to support the club as it tries to lift itself off the bottom of the ladder after slumping to four consecutive losses.
"But I just hope that the fans back the decision we've made and that they support Frank and support the club and we can turn things around because we're determined to do that."
Farina, who arrives in Sydney from a coaching stint in Papua New Guinea, took to Twitter to address the reaction.
"Thanks to the well wishes. Will try to respond later. To those who are not well-wishers, that's fine too. See you Sunday @SydneyFC," he tweeted on Wednesday.
Pignata said there was scope for Farina to stay on past this season if he delivered good results and while there wasn't specific targets he needed to meet, finishing in the top six and making the finals series was a priority.
"If things improve and change then he's in the driver's seat (to stay on)," Pignata said.
"We haven't really set criteria but if he gets them to the top six then it's a great result for us from where we are at the moment.
"Once you're in the finals anything can happen."
Farina, who coached the Socceroos from 1999-2005, takes over from caretaker coach Steve Corica, who will return to his role as an assistant.
He arrives in Sydney on Friday night and will have only one session with his new charges before the Sky Blues face Melbourne Heart at Allianz Stadium on Sunday.
Pignata was confident Farina could handle the pressure that comes with the job and with coaching a side which includes Italian superstar Alessandro Del Piero.
"Frank's coached at a high level," he said.
"He's coached the national team for six years, he's coached high profile players, he handles the media.
"These are all attributes we liked in Frank and he's also someone determined to get results."