The Bones have yet to win in the BGB Southern League Division One Midlands this term.
But they did pick up their first point and clean sheet on Bank Holiday Monday with a 0-0 derby draw at Woodford United.
And Dunion's side will be confident of getting that first win when they face Essex Senior League opponents Hullbridge Sports at Cecil Street in the preliminary round.
"My record in the FA Cup is hardly nosebleed territory," said Dunion. "I think the best I've ever done is the third qualifying round.
"But a cup run would be very important for this club this season in more ways than one.
"Not only would it increase confidence in the players and, hopefully, see them take good cup form into the league games, it would a big incentive financially as well which is something this club needs.
"I think the financial constraints that we are under here have been well documented.
"But the financial rewards for a cup run are good now and that's what it's so important that we perform well tomorrow."
Hullbridge are one level below Rothwell in the pyramid and beat South Midlands League side Leverstock Green in the extra preliminary round of the competition to set up this tie.
So far, they have a 100 per cent record in their league – but they have only played one match due to cup commitments.
But with the higher-league experience and home advantage Rothwell should have enough to prevent the tie from turning into a potential banana skin.
"I would expect us to be winning this game," said Dunion.
"Of course, cup-ties can be funny sometimes.
"But we really shouldn't be nervous going into a game like this.
"I hope that it will have a more immediate benefit of us turning in a real performance of the standard we are capable of.
"Individually, I've no problem with any of the players I have in the squad.
"But as a team I still feel we are under-achieving so this sort of game
is the ideal chance for us to put that right."
Dunion also again called on the people of Rothwell to come and
get behind the Bones and help them push their season forward to achieve the sort of results he feels they are capable of.
"Crowds have improved. But we still need to get more people in through the gate," he said.
"It's never easy for players to perform to their peak in a quiet
stadium.
"With a decent crowd noise behind them, they can go out and produce their best."
Despite his confidence for this weekend's tie, Dunion will be forced into several changes from the team that played at Woodford.
Robbie Maddox starts a three-match ban for his opening-day red card at Arlesey Town while Michael Boyle-Chong (ankle ligaments), Pete Sneddon (knee), Andy Brown (back) and Rashid Koriya (shin splints) are all out.
Liam McInally has returned to training but is not yet match fit.
But Mark Burrows has shaken off an ankle knock and fellow defender Mark Hackett is also back.
Rothwell from: Smith, Malong, Wilkinson, Flannigan, Pownell, Burrows,
Hackett, Glass, F Koriya, Marlow, Bridgeford, Difante, Byrne, Greasley, Kennedy, Rice.
Click here for our Bones site.
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