Wigan Athletic stunned the Toffees to claim a 3-0 victory at Goodison Park this afternoon and end Everton's chances of silverware this season.
Moyes has admitted that his side were not good enough today but thinks that they are still capable of recovering to finish the campaign strongly.
He told the club's official website: "We have to pick ourselves up. We have had a pretty good season, we've not had many downsides but today is a massive one, for me, the team and the supporters.
"We didn't play well and if you don't play well you are going to lose. That's it very simply but that's the case. We would normally do better and play better but it was a big off day. Even when we did try to put a bit of pressure on the shots we had were wide or saved.
"The whole team is in it together now, not any one player. We will pick ourselves up and bounce back. We had disappointment last year and we will try and do a similar job and finish the season well."
Moyes's men are back in Premier League action next weekend at home to defending champions Manchester City.