Warnock signed a two-year deal at Palace to make a surprise return to the club four years after leaving when they fell into administration.
Parish turned to Warnock after giving up on the idea of appointing Mackay when the Scot admitted to sending a series of "completely unacceptable" text messages during his time in charge of Cardiff City.
"Malky interviewed very well," said Parish. "From a footballing point of view he was a very good candidate, but it was impossible to offer him the job."
When Warnock ended his last Palace reign he moved to Queens Park Rangers, who sacked him in January 2012 with the club 17th in the Barclays Premier League after he had guided them to the top flight for the first time in 15 years, and went on to work for Leeds United.
At the age of 65, Warnock is unlikely to prove the long-term solution that Palace were aiming for, but he could have a kingmaking role next summer when he and Parish consider the club's long-term future.
In the short term, the pair were preparing to discuss transfer targets ahead of Monday's deadline. "I think he's got unfinished business," added Parish. "I think he likes the club and has a lot of affection for the fans and he felt a good fit."
After Mackay, Tim Sherwood, Neil Lennon, Steve Clarke and Glenn Hoddle were also linked to the position.