Three goals in four first-half minutes from Maynor Figueroa, Callum McManaman and Jordi Gomez settled the quarter-final contest and prevented Everton from back-to-back Wembley appearances.
An expectant Goodison Park was left stunned and the stadium was virtually deserted by the final whistle with only the visiting supporters celebrating their first-ever semi-final appearance.
"Wigan played well and on the day we didn't play well," Moyes said. "We've not had many of those days this season, probably not had many of those days since January last year.
"Today was one of those days where it didn't go well at all and we just didn't perform.
"We were fortunate as they had hit the post (before the goals) but there were one or two signs we were getting organised to deal with it but we were soon a couple of goals down.
"I thought we tried everything we could at the start of the second half but on the day we didn't make the goalkeeper work hard enough.
"We can't argue, Wigan were the better team on the day. We can't complain, we weren't good enough.
"We never really got to grips with the game. We just didn't look as if we had the creativity which would make that happen.
"When you lose one goal you're saying, 'Calm down, it's not the end of the earth', but unfortunately we conceded by giving a really poor second goal away."
The boos rang around Goodison Park at both half-time and full-time and many fans questioned Moyes' team selection after he opted for Phil Neville, withdrawn at half-time, instead of Darron Gibson.
In truth most players failed to produce the kind of performance usually associated with the teams Moyes puts out but the manager refused to criticise anyone.
"This is a team here, we work together as a team," added the Scot. "We don't point the finger at anyone - I might do in the dressing room but I won't do it publicly. We know where we didn't do well enough today."