Chippenham have lost their place in the FA Cup for fielding an ineligible player during the qualifying rounds.
Defender Curtis Jack was suspended by both Somerset and Gloucestershire Football Associations for non-payment of fines dating back to last season.
Chairman John Applegate insisted they were unaware Jack was unable to face Wells, while Gloucestershire FA had wrongly listed him as Jack Curtis.
Wells will now face Woking in the second qualifying round on Saturday.
The Southern League could also issue its own punishment to the club as Jack also featured in a number of league fixtures.
Speaking about the incident last week, Applegate told BBC Wiltshire: "I'm embarrassed and it's a great sadness to us all."
Chippenham have not been fined for the incident but have lost the £3,000 prize money they were awarded for progressing after their 3-0 win.