Goals from Mauro Zarate, Stewart Downing and Carlton Cole secured the points and lifted the pressure on West Ham boss Sam Allardyce while piling more on to beleaguered Palace.
The Selhurst Park club lost manager Tony Pulis, who guided them to 11th place last season, just before the new campaign started, while sporting director Iain Moody resigned on Thursday over offensive text messages he had exchanged with then-Cardiff City manager Malky Mackay whilst working at the Welsh club.
To compound Palace's misery, they were poised to appoint Mackay as manager when details of the text controversy emerged.
They were forced to pull out of the deal, dragging the club into the Mackay media frenzy and sending the search for a new manager into disarray, much to the supporters' dismay.
"I won't hide behind excuses but it's been a tough week for them (the players)," Millen told a news conference after a game in which Marouane Chamakh's second-half goal to briefly make it 2-1 was the only cause for celebration for the home fans.
"We never really got going today. We were flat. We never really got any sort of tempo and allowed West Ham to control the game. In general, we were lacklustre.
"I tried to play it (the text controversy) down before (the game) because in training they've been fine but when you come to matchday you're never quite sure how they're going to respond.
"It's been a shock to everyone, the circumstances of Tony (Pulis) leaving and then the situation with Malky (Mackay) but I don't think it's going to drag on. Once we appoint a new manager I think it will be a fresh start."
Millen took charge of the Palace's first game of the season at Arsenal last week, where his spirited team looked to have secured a surprising draw before Aaron Ramsey's stoppage time goal secured a 2-1 win for the home side.
The caretaker manager said he did not know who was going to be appointed as Pulis's successor but added that he would be open to the chance of making his temporary position permanent.
"The last couple of days the chairman (Steve Parish) has left me to prepare for the game today," Millen said. "We obviously have to speak to the chairman tomorrow to see what his thoughts are going forward.
"I know from my personal conversations what he's looking for. If he feels I'm the right one then I'll talk to him again.
"I don't think today's result or performance has any real reflection on me or my chances. One result doesn't determine whether you're the right manager or not.
"If the chairman doesn't find the right person I don't think he'll rush into it. He hasn't done that before and he won't do it (now)."
Millen said he expected to manage the team at Walsall in the League Cup second round on Tuesday, as Palace continue to search for the right man to put an end to their misery.
REVERSAL OF FORTUNE
West Ham had endured their own difficult build-up to the new season, with Allardyce under pressure from the club's owners and supporters to play a more attacking brand of football after they flirted with relegation in the last campaign.
A 1-0 home defeat by London rivals Tottenham Hotspur on the opening day, after conceding a stoppage-time goal having missed an early penalty and played against 10 men for over half an hour, indicated that Allardyce's own position may be precarious.
But a display of invention and attacking verve from debutant Zarate and an impressive performance by fellow new boy Senegalese midfielder Cheikhou Kouyate on Saturday suggested a more exciting campaign could be in store for the club.
Allardyce said it was the way his team played, and not the circumstances of Palace's week, that saw a comfortable win.
"We all suffered badly last week by both losing in the last minute of the game," he told reporters. "Maybe we made Palace look lethargic with the quality of our football.
"The whole team played well. It was a very important result and a very important performance. It's been an outstanding day for us after a disappointing result last week."
Allardyce's men host third-tier Sheffield United in the League Cup on Tuesday, hoping for more goals to please an expectant Upton Park crowd.