Goodison fans had their hopes of a trophy dashed last weekend when Wigan dumped them out of the FA Cup.
Moyes said: "Maybe our squad strength is catching up on us. We are running out of legs a little.
"If you are the manager you have to expect the criticism, but it's not something you've seen very often here at Everton. You are not seeing a bad brand of football at Everton - the image of this club being in crisis is completely wrong.
"Everton during the 80s had great teams and great hope but there wasn't too much since then. Now there is a bit of hope.
"This season we have provided the hope that we can maybe get back to those days and so, after a performance like that, the fans are going to be disappointed."