The Toffees were eliminated from the competition at the hands of Wigan on Saturday, and their manager is looking for a quick response with a Europa League place still up for grabs
The Latics scored three goals in four first-half minutes at Goodison Park to deny the 2009 runners-up another trip to Wembley.
And Moyes, who admitted his side deserved to be knocked out of the competition, hopes the result will not affect the rest of the Toffees' campaign as they continue their pursuit for European qualification.
"We have to pick ourselves up," Moyes told the club’s official website. "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.
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"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."
"It just wasn't to be our day, but I have got to say Wigan played well in the first half. They passed it well and had a good chance before they scored.
"The quick goals came and because of that it made it a very difficult task in the second half. The players tried to get back into it but the longer it was going on the more it drained away from us.
"We didn't really create a lot of chances, we didn't threaten as well as we would have liked. We tried to score any way we could but everything we hit went wide or was blocked."
Following Liverpool’s 3-2 win over Tottenham on Sunday, Everton were leapfrogged by their Merseyside rivals in the Premier League table and pushed down into seventh spot.
The Toffees failed to qualify for Europe last season thanks to the Reds’ League Cup victory, and Moyes is keen to seal the deal this term.
He added: "The whole team is in it together, 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."