Millen is concerned the new manager may wish to change the team’s style of play and will not have the opportunity to bring in suitable players before the end of the month.
Pulis departed Selhurst Park on Thursday, reportedly unhappy at the club’s transfer policy.
Millen took temporary charge against Arsenal, just as he had done when Ian Holloway left last year, but could not gain a positive result as Palace were beaten 2-1 at the Emirates Stadium by a stoppage-time goal.
Palace co-chairman Steve Parish indicated the board are looking for someone with experience of the English top flight, with former Cardiff boss Malky Mackay and ex-Tottenham manager Tim Sherwood thought to be the leading candidates.
Millen will hold further talks with the board on Monday, but his main concern is Palace will repeat their poor start from last season.
He said: "This is the problem with changing managers. You bring in players to suit the system you play and if you are bringing in a different manager with different philosophies, then maybe they won't suit that.
"With the window shutting at the end of this month, the appointment is important so they have a little bit of time to bring in new players.
"The players will want to know on Monday which direction the club is going. There is a good group there, but they do need leadership.
"Whoever comes in, it needs to be pretty quick. The longer you leave it then it can start drifting.
"We don't want to be like that and get off to a poor start like last season."