The young Magpies beat their Leeds United counterparts 4-1 last weekend to set up Sunday's tie, which kicks off at 2pm (BST), and while Covid-19 regulations mean there won't be a crowd there, it will nonetheless be an occasion to savour for the Toon teenagers.
In an attempt to prepare the players for the experience, Winskill took them to the stadium on Saturday morning to get an early look at the pitch and facilities - but other than that, he has aimed to keep the days leading up to the game as normal as possible.
"The staff and the players are really excited about being in the next round, and the fact that it's at St. James' Park makes it so much more special - but we have to just treat it as another game, and think about the performance rather than the outcome," Winskill told nufc.co.uk.
"It's the staff's job to try and make sure that everything's as consistent as it has been throughout the season. So the training week is the same, the process of meetings is the same; the thing that changes is the fact that it's at the stadium and there's obviously more riding on the game than a normal league game.
"But the lads have to just concentrate on getting their individual performance, and the collective performance, the same - if not better - than last Saturday. That's been the talk.
"We spoke to them this week about the things that they did well on Saturday, and the things that got them the performance and the result that they had.
"It's important that we look back at those things and catch them when they're good - but it's also important that we focus our attention on the next game. Getting back-to-back wins is important for us, and looking at the season as a whole, it's something we haven't done very often. So that's been the message: last Saturday was good, but it was last Saturday and there's another game to win. The best players and the best teams can reproduce time after time, and that's what we've been focused on this week."
Watford's under-18s beat Colchester United 2-0 in the third round before a 3-2 extra time victory at Lincoln City last month, and play in the Professional Development League - a division below Newcastle.
But Winskill insisted: "Part of the values of our club is that we respect every opponent that we come up against, regardless of what league or level they're from, and certainly in cup competitions, anybody can beat anybody on any given day.
"So we totally respect Watford. They've done terrifically well, just as we have, to get to this stage. They played well and dug a result out in the last round, against a team who we've played in a friendly and know are a good side, so we will treat them on their merits and give them the respect that they deserve. Likewise, they'll do the same to us - and may the best team win."
The Hornets are broadcasting the game live on their official YouTube channel and this prestigious tournament has traditionally been a platform for young players to make their name.
A teenage Paul Gascoigne helped the Magpies lift the trophy in 1985 - with a two-legged final victory against Watford - while Manchester United's famous 'Class of 92' came to the fore seven years later.
Last weekend, Dylan Stephenson's hat-trick against Leeds suddenly brought the 18-year-old to the attention of Newcastle supporters all over the world and Winskill - who played in the competition himself for United in the 1990s - revealed: "Jamaal Lascelles came into the dressing room before the game on Saturday and kindly spoke to the lads, and one of the things he spoke to them about was the fact that it's a great window of opportunity for them to go and show what they can do to a wider audience of people who may not watch their games as frequently.
"That was certainly the case for the group on Saturday. Individually and collectively, it was a really positive week and people have rightly said how well they played - Dylan included in that - but it's history now, it's gone, and they've got to do it again. If they want a career in the game, you have to be able to produce on a weekly basis, and that's what they have to do, while taking as many positives as possible from last week.
"In every round we've played in, there's been a carrot at the end of it; we knew if we could beat Huddersfield (at the third round stage), we might get a home tie, and we did. That home tie was at Whitley Park but the next carrot was if we won that game, we go to St. James' Park for the next round. The carrot for this round is hopefully we can get another game at St. James' Park - and if there was a crowd there, that would just make it even more memorable.
"That's what this competition is, for the young players who will make a career at Newcastle or elsewhere; it will create memories for them."
UEFA Pro Licence holder Winskill replaced Dave Watson as lead under-18s coach in the summer of 2019, having previously worked with various different age groups at Little Benton, and he added: "This group has been together for a long time and I've been with them for quite a long time as well. We already have some fantastic memories of winning tournaments in France, in Poland, of going across to South Korea and playing a tournament there.
"But you want those memories to be winning memories. Those are the ones that will stick with you, that the lads will talk about when they bump into each other 20, 30 years down the road. They'll talk about the time when they were at Newcastle - hopefully some of them will have been in the first team by then, but they will still remember those great times and it's up to us to help the lads create those for everybody."
