Goals from Marouane Fellaini and Nikica Jelavic ensured Everton only their third win in 10 games at the weekend and cemented their fourth place, and Moyes says: “When it got to 70 minutes it looked like it wouldn’t be our day. We were looking to see how to alter it.
“I didn’t think we were playing that badly but we conceded before half-time and were left chasing the game. There’s a great deal of belief and confidence.
“We have always given the top four teams tough games. Maybe you could say our record against them isn’t that good, but at least we give them a game. Now maybe teams will come to Goodison and make it tough for us.”
It isn’t the first time this year that either Fellaini or Jelavic has made a telling contribution. And having previously relied heavily on Leighton Baines for inspiration, Moyes takes heart from the breadth of influence now available.
“We are an improving team,” he says. “We kept going and we have players now who individually can make something happen.
“A lot of the time it has been Leighton Baines who has down something special, but now we have Kevin Mirallas and Jelavic, and Fellaini is now making himself a more important player.”
Nevertheless, Moyes is acutely aware hopes of success will rely on ensuring the core of his squad remains fit and in form for the majority of the campaign.
After all, the League Cup defeat at Leeds United in September underlined Everton simply do not have strength in depth comparable to their main rivals for a top-four berth.
“I wouldn’t say our squad is big enough, but I would say we have got good quality,” says the Goodison manager. “I have 15-16 players that I can call on. The staying power I’m talking about is different. People will drop out of form a little bit, and do you have other players to bring in or do you have to have players playing through it?
“Maybe we don’t have the luxury to take our best players out of the team. We have to hope they stay in form, stay fit and avoid injuries.
“You want players to come in and make a difference. And we brought in young Apostolos Vellios against Sunderland and while he didn’t score we managed to get the two goals when he was on the pitch.”
Another player to have emerged from the bench at the weekend was Thomas Hitzlsperger, the former Germany international making his debut having recently signed a short-team deal following an extended trial.
The 30-year-old will hope for further involvement on Saturday when Everton aim to extend promoted Reading’s winless start to the Premier League campaign at the Madejski Stadium.
“The whole time I’ve been here, it is such a good place to be and I want to play more and contribute more to the club’s success,” says Hitzlsperger. “I was delighted to get on the pitch as I’ve been waiting to get a chance for a long time.”