The defeat, which came after goals in either half from Saido Berahino and Gareth McAuley, is their seventh in a row, leaving them rooted to the bottom of the Premier League.
The fixture at The Hawthorns was Millen's second game in charge following Ian Holloway's departure and, after a 2-0 loss to Arsenal in his first, the stand-in coach is eager for the new boss to come in and turn things around.
The 47-year-old was, however, full of praise for Palace's players after a week once again filled with plenty of speculation.
"To be fair, the players have been great this week, it is not an easy situation with all the speculation around when the manager's going to come in, who it is, so the players have been focused," Millen said.
"I don't think you can accuse them of not concentrating on the job in hand but it's a tough time for everyone at the club really and the chairman's not going to rush into it.
"He needs to appoint the right person but I think the sooner the better someone does come in with new ideas, a fresh voice, hopefully a little bit of luck maybe that I don't think we are getting at the moment, and things can change.
"I spoke to the chairman on Friday, he's busy doing what he needs to do, and he said to me to continue this week with training ready for the Everton game (next weekend)."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.