Newport boss Michael Flynn maintains the club cannot afford to prioritise promotion from Sky Bet League Two over a lucrative FA Cup run.
The Exiles are set to host Premier League Brighton on Sunday night, which will bring in significant additional revenue from being one of the eight primary match selections for broadcast.
In 2018, Leeds were beaten at Rodney Parade followed by a draw against Tottenham and a trip to Wembley for the replay.
The next season, both Leicester and Middlesbrough were defeated when they came to Wales, with Manchester City eventually proving a tie too far as Pep Guardiola's side won 4-1 in the fifth round.
Those memorable performances helped Newport clear their substantial debts and start to look up the table rather than just battling to stay in the division.
Flynn's side are well set for a promotion push in 2021.
The Exiles are currently second in the table, just a point off top spot and with a match in hand after having their last two league games postponed because of the weather.
The Newport boss, though, will always look at the bigger picture of what securing more income from the FA Cup could do for the club.
"We cannot afford to dismiss the FA Cup because of what it means for finances," Flynn said.
"If you go back two seasons to when we played Tottenham, that draw was more important than getting promoted. That is the financial implications we have to deal with at this level.
"It would be nice to have that conundrum where you can just pick the league over the cup competitions, but whatever team come here, I know (Brighton boss) Graham (Potter) will have them taking it seriously.
"He will not be taking his foot off the gas, they want to win this one – and have two tough Premier League games after this.
"We want to upset them and get into the next round of the cup."
Former Swansea boss Potter is expected to utilise his squad for Sunday's match, but remains determined to use the FA Cup to help provide a boost for Brighton's top-flight survival battle.
Flynn added: "It can be done, but maybe it is different again down the bottom end of the Premier League, because if you do go out of the Premier League, that can be financially ruining as well.
"It is a tough conundrum for clubs for different reasons all across the country."
Whoever plays for Brighton, Flynn knows his team will have to be on top form again to stand any chance of making it into the fourth-round draw.
"Brighton are littered with top players, as you expect being a Premier League team – but it is Rodney Parade and we know anything can happen there," he said.
"Every time the boys have risen to the occasion (in the cup games), they have not been startled, have been on the front foot, raised their game and shown they are good players."
Flynn continued: "We will miss the crowd (on Sunday), football is not the same without them.
"But we are playing a Premier League team at home, live on television, and there is still a buzz here.
"We are all still excited – it is the best cup competition in the world."
As well as preparing for Sunday's clash, County have also been busy in the transfer market and completed the signing of midfielder Jack Evans from Swansea on Friday.
The 22-year-old has made the move east on a permanent deal that runs until the end of the season, while striker Jake Scrimshaw has arrived on loan from Bournemouth.
