The Dolly Blues manager, who has been in charge of Nelson and Ramsbottom United in the past, has never won a match in the competition in six years.
The prospect of him ending that run did not look promising as City were held at home by North West Counties League outfit Northwich Victoria on Saturday.
However, they produced a much improved performance in midweek to win the replay 2-1 thanks to a couple of goals from David Norris.
“From a personal perspective, it’s nice to get that record, that jinx, out of the way,” said Fell, whose side will now take on National League North outfit Spennymoor Town at Giant Axe in the second qualifying round.
“I had three years with Nelson and three years with Ramsbottom and I was always on the wrong side of the margins in the FA Cup. That happens.
“From a team perspective, we weren’t at the races on Saturday, albeit we still had chances to win the game although alternatively, we could have been out of the cup.
“But we were fantastic on Wednesday night to be fair. The lads showed the difference in class which there should be when you are two leagues apart.”
Currently in 10th spot in the NPL Premier Division table after six games, City have enjoyed a satisfactory start to the season according to Fell.
They have accumulated 10 points and are only five points off leaders Hyde United with a game in hand.
Fell has challenged his men to remain in touch with the leading teams, starting by picking up three points at home to Grantham Town, who are a point below them, on Saturday.
“I think it’s only after the first 10,12,15 games that we will start to know the sides which are going to be up there,” said Fell, who revealed striker Brad Carlsley faces four weeks on the sidelines.
“If we can be in touching distance after the first 10 games, we have a chance of being in the mix.”
Elsewhere, in the NPL North West Division, Clitheroe host Runcorn Linnets and Kendal Town are at home to Pickering Town.
Longridge Town host AFC Blackpool and Charnock Richard are away to Prestwich Heys in the FA Vase second qualifying round. Garstang and Burscough have no games.