The League One side shocked Liverpool in the last round and will be looking to follow up their 1-0 win at Goodison Park in the third round five years ago.
"We know what they can do as they did very well against Liverpool. It was a great result, but that's what the cup does," said Moyes.
"We've been knocked out by Shrewsbury (third round in 2003), knocked out by Oldham.
"I thought we'd prepared well when we went to play Shrewsbury, and again when we played Oldham, but we didn't get the result, and that is football.
"You have to play well, take your opportunities when they come along, which is cup football because you only have one chance.
"So we have been there, done that, we know what it's like and we don't want it to happen again.
"We'll do everything we possibly can to make sure it doesn't."
However Moyes insists a top-four finish in the Premier League remains his priority this season.
"Qualifying for the Champions League always means more because the financial rewards from that are far greater than what you get from the FA Cup," he said.
"We can think of a lot of teams who have won the FA Cup and it's not desperately changed their fortunes, whereas qualifying for the Champions League does.
"If you do that, and you get into the group stages...look what it has done for Celtic, the profits they have made over the last six months, with most of it down to how they have done in the Champions League."