Allardyce resigned from Palace in May after keeping the club in the Premier League and said he had “no ambitions to take another job”.
Palace are due £2million in compensation after the 63-year-old took over at Everton last week and Parish said: “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.”
Parish has also praised the impact Roy Hodgson has had at Palace, who moved off the bottom of the table last weekend and play Bournemouth at home on Saturday.
“I think the players trust him, they believe in him and they can see that things are improving,” said Parish. “The enthusiasm he has got for everything he does is a joy to see.”