The League One outfit travel to their Premier League counterparts in the second round on Wednesday.
"It will be a great occasion but it will only be truly remembered if we deliver a performance to be proud of," Evans is quoted as saying by Sky Sports News.
"We will need every player to be at their best and we know we need Aston Villa to have an off night. We will be in their faces all over the pitch and hopefully they won't be ready for that.
"I believe it can happen, but we have to have a top, top night."
Rotherham defeated Sheffield Wednesday 2-1 in the last round.