Goals from Saido Berahino and Gareth McAuley left the Eagles rooted at the foot of the Premier League standings.
Palace, lacking creativity and any forward force, produced little to test West Brom goalkeeper Boaz Myhill as they slipped to a seventh successive defeat, leaving them six points adrift of safety.
With the search for Ian Holloway's successor still ongoing, the club's future looks precarious and, after declaring himself out of the running for the permanent post, caretaker manager Millen confirmed there is no appointment imminent.
And Millen has called for an experienced manager to be brought in at Selhurst Park.
"I'm just taking it day-by-day," he told Sky Sports. "As far as I know I am preparing for training this week for Everton at the weekend.
"We'll analyse today's game and the players will be in on Monday to look back at what went wrong.
"When you look around the club in general, there is not much Premier League experience all round.
"Maybe it needs someone who knows what it takes to win at this level, someone who has been here at done it at the top level."
Despite admitting he is not the man for the job, Millen does hope to remain at the club in a coaching capacity, but concedes he has no guarantees.
"I haven't had any assurances," he added. "When the new manager comes in we will sit down the chairman and see where I stand.
"I am hoping I will be able to open discussions with the new manager and chairman about my role and we can take it from there."
Despite suffering their seventh straight defeat of the season, Millen insists there has been an improvement and believes the Eagles have deserved more from their last two outings.
"The reality is the quality in the Premier League sometimes hurts you," he said.
"The corner we conceded the second goal from was quality, the delivery and aggression to attack the ball, you have to hold your hands up.
"But the effort, togetherness and commitment deserved something from the game. I feel sorry for the lads because the last two games we have had chances but got nothing.
"Performance wise against Arsenal, we deserved something and again today it was small margins."