Despite the defeat, it was a superb performance from Everett at centre-back.
She made a number of vital interceptions and blocks in the Palace box - but Laia Codina and Stina Blackstenius scored to earn the visitors a place in the semi-final.
Speaking about the game, Everett said: "We always knew it was going to be tough, playing one of the best teams in the world, but I thought the girls put in a massive shift and stuck to the game plan.
"I thought we were the better team in spells, but when you're going for it at the end - we conceded that last goal, which kind of killed it."
