Despite suffering relegation from League One last season, the Spireites twice beat Rovers at the B2net Stadium.
John Sheridan's side triumphed 4-3 in the Johnstone's Paint Trophy, before March's 1-0 league triumph brought about the downfall of Moore's predecessor Les Parry.
"It's not the easiest draw, but then there aren't any easy cup ties," Moore told Tranmere's official website. "You always want to be drawn at home, but we'll go to Chesterfield aiming to get through to the second round.
"Everybody will want to go into their opening league games on the back of a win and a good performance and we'll be the same.
"We've got the benefit of having played them three times last season so we'll know a bit about what to expect, but it will be the same for Chesterfield. It's still a long way off though and there's plenty of work to be done before then."
