Despite reaching the fifth round for the first time in nearly three decades, the club will be pointed back towards their next league fixtures by their hard-nosed manager.
John Windass’ first-half strike secured a 1-0 victory over fellow promotion hopefuls Ipswich Town at Stok Cae Ras, sending the Dragons into the last 16 for the first time in 29 years.
Yet, while the result added another chapter to Wrexham’s remarkable rise, Parkinson was quick to stress that league matters take precedence.
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Windass converted after 34 minutes in a tightly contested encounter, settling a clash between two sides who will renew hostilities in the Championship at the same venue next week.
Ipswich boss Kieran McKenna’s decision to make 10 alterations to his starting line-up underlined where his priorities lie — and Parkinson echoed that sentiment when assessing Wrexham’s own path forward.
Before kick-off, the occasion had been framed as an opportunity to carve out a slice of history.
Manager Parkinson said: “We spoke before the game about our chance to create a bit of history.
“We’ve done it and I’m so pleased because it was always going to be a tough game against a very good side.
“Every season in football is special and you’ve got to savour it.
“This season, with the challenge of being in the Championship and now an FA Cup run, we want to enjoy it, and tonight we certainly did.”
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The victory comes during the fifth anniversary week of Wrexham’s takeover by Ryan Reynolds and Rob Mac, a period that has seen the club surge from the National League to sixth place in the Championship after three successive promotions.
With momentum building and the Premier League now a realistic ambition, cup success is a welcome bonus — but not the central objective.
Parkinson said: “I think it’s great for our owners, to get them into the fifth round.
“We can really look forward to the draw on Monday night when we’ll be in a hotel in Bristol.
“We’ll savour that but, obviously, it’s the back-burner now for the FA Cup and we’ll concentrate on the league.
"In general I thought we showed how we've evolved as a team since we played them down at their place where we were excellent, detailed, out of possession.
"But tonight with the ball I thought we were really good at times and that's what we're all about.
"We're evolving as a team into this level and I enjoyed watching some of the football tonight."
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While Wrexham celebrated progression, Ipswich’s attention remains fixed on securing an immediate return to the top flight.
The Tractor Boys sit third in the table and face a pivotal league meeting with Wrexham in the coming days.
McKenna defended his selection choices and broader strategy.
He said: “We had two goals. We wanted to go through in the cup and we tried right until the last second to do that, but a big priority had to be getting minutes into players who needed it and to protect some other players.
“I know if you go out and you make changes you have to go win the next league game, then there won’t be too many questions.
“But if you look at the schedule and where we would fit in the games for an FA Cup run, to be honest, it was really hard to see how that wouldn’t be to the detriment of the group.
"It (performance) was mixed. I thought we started both halves well and I thought we started the game well and had a couple of early chances.
"I thought we came out really strong in the second half as well and were close to getting the goal.
"But they had some momentum as well, we know they can do that here and the atmosphere was good.
"Second half, we tried everything but we just couldn't get it over the line."
For Parkinson, the cup run is a milestone worth appreciating — but the greater prize lies elsewhere.
With promotion firmly in sight and another crucial Championship fixture looming, Wrexham’s manager has made clear that the FA Cup, for now, must wait.
