At the end of last season, Allardyce ended his time with Palace and claimed that he intended to retire from football, but the former Eagles boss has just moved into the dugout with the Toffees.
However, Parish has suggested that he has no issues over Allardyce's U-turn, acknowledging that Palace are now due compensation from Everton due to the terms of his previous contract.
Parish is quoted by the London Evening Standard as saying: "We are very comfortable with the situation and, apart from against us, we wish him well.
"Everyone knew what the deal was. We should be reasonably compensated by Everton."
Allardyce will not face his former club until the two teams meet at Goodison Park on February 10.