The Toffees have won just two of their last seven matches, and were dumped out of the FA Cup by Wigan Athletic last weekend.
Their inconsistent form has also seen the Merseyside club fall to seventh place in the Premier League table, and Moyes believes that the lack of depth in his squad is being exposed.
The 49-year-old told the Daily Star: "There has been criticism, but maybe our squad strength is catching up on us.
"If you rotate your squad in the early rounds and get knocked out, people ask why you have changed the team. I changed a couple at Leeds and we lost, so I made the decision afterwards not to change the team too much.
"We are probably finding that out now and running out of legs a bit."
Everton can move to fifth place in the league with a win over Manchester City on Saturday.