The draw was screened live on Periscope via the Somerset FA's Twitter feed and sees the Grove along with six other clubs miss out on a first round game and progress straight to round two.
Among those clubs also not in action are Yeovil Town, Taunton Town and current holders Weston-Super Mare, who won the cup last week in a final delayed from last season. Last season saw Hengrove go out to the eventual winners in a 4-0 defeat at Paprika Park.
Ties for the first round will take place in the week commencing 7th October 2019.