Having lost their last seven games on the bounce, the hosts came into the game as underdogs, but had the better openings over the course of 90 minutes with Marouane Chamakh, Jerome Thomas and Kagisho Dikgacoi all coming close.
The result earned Palace their first Premier League clean sheet of the season and Millen was proud of the display despite their frustrations in front of goal.
"The 11 that started, the subs that came on, and even the subs that didn't get involved were behind the players, so I'm very proud of them," he told Sky Sports.
"It's nice to come in here with a smile on my face having actually some points from the game and, if we're being greedy, when you look at the clear-cut chances, we should have won the game.
"We got in some good areas and there's two or three I've seen on the replays that if you're going to be critical, we have to start taking those chances.
"We've had that in a few games now and they're the key moments that we're not taking, but on the flipside, keeping a clean sheet will give everyone a big boost and I'm so pleased for the players.
"We've worked hard on our shape - we know Everton were a good passing team so we tried to block it up essentially and I thought we did that in general.
"But also we counter-attacked and we opened them up, and we have got to start taking those chances because the lads deserve that."