FA Cup First

What I did gather from the "Football in Manchester" TV series that the first Manchester team to enter the FA Cup was back back in 1877. The 7th year of the competition. On the 3rd November, Darwen v. Manchester FC. The notable rugby club fielded a team for the 11 a-side game. Didn't win, lost 3-0.
Manchester Rugby Club.
FA Cup Results 1877-78 season