Warnock signed a two-year deal at Palace on Wednesday to make a surprise return, four years after leaving when the Eagles slipped into administration.
He moved on to QPR, who sacked Warnock in January 2012 with the club 17th in the 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 but achieved scant success at Elland Road.
Parish turned to Warnock after giving up on the idea of appointing Malky Mackay when the Scot admitted to sending a series of "completely unacceptable" text messages during his time in charge of Cardiff.
Palace will face Newcastle United in the League Cup as the Third-Round draw was made on Wednesday.
Another long trip for the Toon travelling supporters.
Chelsea v Bolton
Arsenal v Southampton
West Brom v Hull
Crystal Palace v Newcastle
Leyton Orient v Sheff Utd
Cardiff v Bournemouth
Sunderland v Stoke
Derby v Reading
Liverpool v Middlesbrough
MK Dons v Bradford
Man City v Sheff Wed
Burton v Brighton
Swansea v Everton
Shrewsbury v Norwich
Fulham v Doncaster
Tottenham v Nottm Forest
Ties to be played on September 23-24.