And Moyes admitted: “We've got four games, three away and the one at home being a derby makes it difficult period.
“The away games have been tough. Wigan are a good team as people will find out, QPR are forgetting better and Fulham are a decent side. There are no gimmes and this is a difficult period for us.
“Most people, me included, would say it has been a far better start than we've had in the past and if we win at Fulham it will be a really good start.”
While Kevin Mirallas is hopeful of recovering from the ankle problem that forced him off at half-time in the derby, Darron Gibson remains some weeks away from a return as he strives to recover from a tendon problem in his thigh.
Meanwhile, Moyes has expressed his sympathy for supporters after Everton’s trip to Southampton was switched to Monday, January 19 for live television coverage – and fears such fixture changes are dissuading fans from attending far-flung away matches.
“Everybody needs the extra TV revenue, especially Everton, so we are not against that,” said the Everton manager. “We're happy to get it, but I've got to say for the supporters to try and go to Southampton on a Monday night is a really tough ask.
“If I was a supporter I'd be wondering how could I get down there for a Monday night and get back for work on a Tuesday morning. I just don’t think you can do it.
“I think it will definitely stop Everton fans from going to the game.
“Maybe Everton fans who live in the London area will go, but for fans in the North West is tough. We've got to watch that it doesn't start to put loyal supporters off.”