Millen took charge as the Eagles pushed Arsenal all the way in Saturday's Premier League opener, before Aaron Ramsey struck a 91st-minute winner to seal a 2-1 win for the Gunners.
The late defeat capped a miserable week for Palace, who saw manager Pulis leave the club by mutual consent just days before the showdown at the Emirates Stadium.
With co-chairman Steve Parish looking on, Millen is hopeful that yesterday's performance will stand him in good stead for when a new manager is named.
"I'd like to continue, I enjoy being in charge," he told reporters. "Whether it's the right time or not [I don't know]. I'll speak to the chairman tomorrow.
"It's been very quick in the last two days, the chairman's not had a chance to talk to the players, to talk to me about his ideas going forward, we just focused on today's game.
"On Monday I'm sure there will be more conversations because the players need to know what direction the club wants to go in and hopefully at the start of the week there will be some more answers."