The Reds beat Ipswich Town 1-0 to progress to the fifth round for the first time in 29 years, and just the sixth occasion in the club's history.
Although the focus is on the Championship play-off push until the last 16 tie which will take place on the weekend of March 7, Parkinson says it is a game everyone can look forward to.
"I'm absolutely delighted with the draw," said Parkinson, who saw his side begin their cup campaign by beating top-flight strugglers Nottingham Forest in the third round.
"It's a brilliant draw for the club, for the owners and for our supporters.
"Everybody deserves that and when it comes, it's going to be a great day.
"It's just a brilliant draw for us, it really is. We said if we got a third home draw on the bounce that would be brilliant for us.
"It's a great progression for the club. We spoke about getting a Premier League club - we hadn't done that since I've been here - and we beat Forest, then we've had to work really hard against Ipswich to get this draw.
"I'm so pleased for everybody connected with the club."
Wrexham twice reached the fourth round before bowing out under Parkinson, who took charge in July 2021, and he says progressing to this stage of the competition is a big deal for the club who are one win away from making the quarter-finals for the fourth time in the club's history.
"It's re-emergence as a football club going into these rounds of the FA Cup," he said.
"All along it's keep testing us as a group and keep putting markers down as a club."
Wrexham drew 2-2 against play-off rivals Bristol City at Ashton Gate on Tuesday in the first game since discovering Chelsea will be heading to north Wales.
Parkinson was pleased with the first-half performance, with his side leading twice before City scored a last-gasp equaliser, and he insists the league is the priority until the cup tie.
"The FA Cup draw is never going to affect our performance level and that's a very good performance against a team who didn't play at the weekend," he added.