The Merseyside club made it through to the semi-final of last season's competition, before suffering a defeat to city rivals Liverpool.
Moyes, however, is targeting another visit to Wembley, even though he understands it might be difficult. He told reporters: “We want to go as far as we can in the FA Cup and we will be doing everything we can to get through. We will not underestimate Cheltenham and we will have to go there and do a really good job if we want to get into the next round.
"Our players have to play - that's what they're here for. Otherwise, they'll be thrust into the really big games and people have to be ready. We'll have a look at it and see what we plan to do in terms of selection.
“We have seen both sides of it. I can go back to ties we have lost in the early rounds of the FA Cup, so we know what it’s like and how difficult it can be.
“It’s not always been the easiest thing in the past – we have lost at Shrewsbury and Oldham – so we are well aware how difficult it will be."
Despite this, Moyes acknowledges that the draw has been kind to Everton.
He continued: “You would like to play at home but when you see some of the real mouth-watering ties – there are some all-Premier League matches – at least we have got a tie where we are playing lower league opposition.
“They have a little bit of an advantage because they are at home but I would hope that our experience and the players we have got can overcome it, albeit it’s never going to be easy."