The London-based outfit sit rooted to the foot of the table having amassed just one victory in 10 attempts so far this season, culminating in Holloway parting company with the Eagles last month.
Keith Millen has stepped into the role on a caretaker basis since, but Phillips believes that it is vital that the club identify a long-term solution quickly in a bid to kick-start their fight for survival.
"It will give everyone a lift when the new manager arrives - the quicker the better," he told the Daily Express
"If the new manager has Premier League experience, then great, but it is quite an art getting out of the Championship. You need to know that league too.
"I know it sounds that I'm already talking as though Palace have already been relegated, but the club does have to look at the bigger picture."
Palace host Everton at Selhurt Park later today.