Town take on the Sky Bet League One play-off hopefuls on Saturday (3pm) and will go into the game as the lowest-ranked team still left in the competition.
“Going into a game of that magnitude, knowing the consequences of what’s at the end of it, that’s enough to excite the players,” Way told iFollow Glovers.
“Players have got the opportunity to create a story for themselves, and it will always be one player. I don’t know who it is, but I’ll be making sure that player enjoys the moment after if it happens.
“I’ve been in a number of situations with Yeovil now, I’ve played in a number of games as a player, so I talked about when I think my first game was against Stevenage in the cup: sense it, see it, feel it.
“And I want the players to sense it and see, and then at the end feel something special, because they deserve it. This is a hard-working group, a young group, but they’re all honest, and what a fantastic opportunity.
Should the Glovers get through to the next round, they have the chance of facing a Premier League side, something Way is relishing.
He said: “You’re 90 minutes away, so hopefully some clown doesn’t fly a drone in again to delay the game!
“One thing that I can trust is that my players on Saturday, against a good Bradford team, will go toe to toe and they’ll give everything to get a performance that will enable us to get into the next round.”