Warnock was confirmed as Tony Pulis’ successor on Wednesday after the Welshman left Palace by mutual consent just under a fortnight ago.
Speaking exclusively to Sky Sports News HQ, Parish declared Warnock the right man for Palace, insisting the 65-year-old - who managed the south London club between 2007 and 2010 - had unfinished business in the Premier League.
“It’s not so much about being relieved, it’s about being happy that we’ve found the right person,” Parish told Sky Sports’ Jim White.
“I’ve known Neil since the club went into administration. He’s someone who’s always been helpful to me and offered advice and I think he’s a safe pair of hands for us right now.
“He’s got unfinished business in the Premier League. As we all know he went down with 38 points, which would have kept you up last year, and in unfortunate circumstances with Sheffield (United in 2007).
“He was out of the relegation zone with QPR (in 2012) when they decided they wanted to go in a different direction so I think he has unfinished business.
“I think he has things he wants to prove to himself. He likes the club, he’s got a lot of affection for the fans and it felt a good fit.
“I think it’s positive all round for the club and I know that the players will be upbeat at the training ground tomorrow so I’m looking forward to Newcastle now."
Parish refuted the suggestion that Warnock was not his number one choice for the job after the club were linked with candidates including Tim Sherwood, Steve Clarke and Neil Lennon.
“You see people and you talk to them and you get an understanding of what they are about and you see the people who are the right fit for your football club,” Parrish said.
“It doesn’t matter who you see first, who you see second, or who you see third.
“We never offered the job to anyone else - no job offer was made to any other manager other than Neil and that’s the person we want to go forward with.
“I think he’s the person that most fits our style of play and tactics. We’re difficult to beat - or we were – and we need to get back to that.”
Parish said former Cardiff manager Malky MacKay had been a strong contender for the job but admitted he was no longer a viable candidate following his recent text scandal.
“From a footballing point of view Malky was a very good candidate. Unfortunately, there were things that meant we couldn’t bring him to the club, so it was never really under consideration once those things became known.”
On the future of caretaker manager Keith Millen, Parish added: “Keith is coming up for a meeting tonight with the chief scout and the new manager.
“Keith has done a fantastic job for us. He’s part of the fabric of the football club and I think we’d certainly like to find a role for him within the new structure.”