The Scot had been in charge at Goodison Park for 10 months when he took his side to Shrewsbury in the third round and saw former Toffees' defender Kevin Ratcliffe, in charge of a side 80 places below in the lower reaches of the then third division, get the better of him.
"I am more wary of what happened against Shrewsbury 10 years ago," said Moyes ahead of the trip to the npower League Two side.
"We went out then so it's happened to us in the past. We have to make sure it doesn't happen - although we were trying to do that then as well.
"There are no guarantees in football, you have to go and earn the right to win the games.
"You like to play at home but when you see some of the real mouth-watering ties which have come out - some all-Premier League clashes - I wouldn't say we've been lucky but at least we have lower opposition.
"It has not always been the easiest thing in the past, we have lost at places like Shrewsbury and we lost at home to Oldham so we're well aware how difficult it will be, no matter who you draw.
"You would expect Premier League players to have the extra quality but is their attitude right, are they prepared for what is to come?
"The lower opposition tend to get themselves a little bit higher and more ready for it as it gives them a chance to showcase themselves and you have to be ready for that."