Boro boss Westley insists he does not see Wednesday night's second-round tie at Goodison Park as a "big day" for the League One club because he knows how badly such occasions can go.
Referring to his time as Farnborough Town manager, Westley recalled an FA Cup fourth-round fixture at Arsenal in February 2003.
"I don't know about a big day," he said.
"I can remember preparing for a big day at Arsenal some years ago. I took my Farnborough side there, we had a man sent off, we got absolutely battered and it didn't feel like a big day at all. It was a horrific experience.
"So I don't look at it as a big day, I look at it as the next game and to win any game you've got to prepare properly.
"You've got to get ready for these games by giving them the respect they deserve. You need to appreciate why those players are at that level and why those clubs are where they are. If we don't do that then we run a big risk."