For the first time this season, Moyes felt Everton had been beaten by a better side in Sunday's 2-0 defeat to Manchester United at Old Trafford.
More troubling to the Toffees boss were the signs of weariness he detected in some of his key players.
After collecting just six points from their last five games, Everton are now six points adrift of Tottenham in the battle for a Champions League slot, and two behind Arsenal, who have leapfrogged above them into fifth.
It is still a creditable effort, and only the foolhardy would write Everton off just yet. However, operating on a budget substantially less than comparable clubs, Moyes has laid bare his worries.
"We are asking people like Leon Osman and Steven Pienaar, who we rely on heavily, and Leighton Baines to put a big shift in and do it for us every week," he said.
"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."