David Moyes and his side of internationals head to the Cotswolds to face a side fourth in npower League Two in front of a 7,000 sell-out crowd and the ESPN cameras in what is the first-ever competitive senior meeting between the clubs.
And Yates, whose Robins have one of the best home records in the division, is not content with thoughts of a few good memories and some positive exposure for the club.
"We won't be going out there saying 'let's just enjoy it and let's take a 2-0 defeat' and be happy with that," he said. "We will go out there having planned and prepared properly and make sure the players do all they can to make sure we give ourselves a chance.
"It is only 11 v 11 and yes, they are Premier League players, but you never know. After 60 minutes if we are 3-0 down we might not believe quite so much but right at this moment in time we have to believe we can do something.
"The cup has got a tradition of shocks, so why not? We want to cause a shock and we know that is a big task. But we know we have the capabilities to do it."
Yates travelled to watch Everton's away win at Newcastle, at the end of an unusual Wednesday which saw him visit one of his former players in Durham prison, and he is aware of the importance of not scaring his players by over-analysing the Premier League side's abilities.
"I'll have a chat with the staff first and see how much we want to frighten them," he said.
"We have got clips and lots of information but we want our lads to be as free and as ready for it as they can be, not to overburden them by asking them to watch (Leighton) Baines when he does this and (Marouane) Fellaini when he does that.
"(The players) know how good (Everton) are, but we'll have key things and we'll play to our strengths. We will try to do things as normal, it is about us."