The Toffees missed out on a place in next month's final after they were defeated 2-1 by local rivals Liverpool last weekend.
Despite a daunting visit to the Premier League leaders, Moyes believes that his team can banish those recent memories with a good performance at Old Trafford.
"It is not the sort of thing you can just shrug off. It was the semi-final of the cup and I think anyone losing a semi-final finds it hard, but when you lose to your neighbours that makes it even worse," said the Scot.
"I actually think after the game we've just had, this is as good as you can get, because we can go there with a little bit of freedom.
"We are not kidding ourselves - it will be a tough game, as it is for every team that goes there, but we'll give it a go and try to show the form we have been in, in the main, over the past few months."
Javier Hernandez scored the only goal as United earned a 1-0 win at Goodison Park back in October.