The Toffees, who have gained six points from their last five encounters in the Premier League, succumbed to a 2-0 defeat against Manchester United yesterday.
Moyes, who is aiming for a top-four finish, believes that tiredness could creep in on his stars at the Merseyside club.
"Maybe the numbers will allow us to have a good half season, but not a good full one. I hope I am wrong. We do tend to finish strongly.
"This time we have had a really good opening, so I hope we can do it again. But we are asking a small number of players to do it for a full season."
Everton are currently in sixth place in the league table, six points away from a Champions League spot.