Pulis was officially unveiled as Palace boss on Monday following Ian Holloway's departure last month.
Parish now believes that the Welshman will shape the team into one that is hard to beat as they look to climb up the Premier League table.
"In terms of the clubs around us, I would like to think Tony is the manager they would least have liked us to get," he told the Evening Standard.
"Tony would definitely have been one of their lowest choices and that was an easy yardstick to put it against. You don't get an easy game against one of his teams."
Pulis takes charge of Palace for the first time on Saturday when they travel to Norwich City in the league.