Elliott Dickman's side currently sit in third spot of Group G on four points and can move above the Hornets' second-string with a much-needed victory at Whitley Park to boost their chances of reaching the last 16.
Carlyon, who signed his first professional contract with the Magpies last summer, is determined for United's youngsters to claim a third successive win in all competitions after Premier League 2 triumphs over Nottingham Forest and local rivals Sunderland in recent weeks.
"The game is important to win to give us a strong chance of qualifying for the knockout stages," the 19-year-old told nufc.co.uk. "We're on a good run of form, winning on Monday, and we'll aim to end the week positively with a win.
"Our team performances have been solid and we've stuck together so I think the team is feeling confident heading into Friday's game.
"We've got a strong squad with a lot of talent within it so I can't see why we can't try to go one better in the competition than what the team did a few years ago (reaching the 2019 Premier League Cup final).
"I think it'll be a good challenge against Watford. It's good when you aren't playing the same teams week in week out so it'll be a different test for us and a one we'll enjoy.
"I think we started the season well, in terms of results, but then our form dipped. Now we have built a platform which we now need to keep up with strong results and performances."
Carlyon was handed his first competitive start of the 2021/22 campaign against Sunderland as the versatile defender - who can also operate in midfield - kept a clean sheet in a 2-0 home victory against their North east neighbours.
The Durham-born teenager expressed his delight in returning to action after suffering a jaw injury during the opening stages of the season as well as coming out on top against the Black Cats.
"It was my first full start since pre-season so it was a good game to come back into. I broke my jaw so I was out for a few months. At the start, I wasn't myself and felt quite down but I picked myself up and after doing my rehab, made sure I came back fully fit and ready to train.
"I was delighted when I found out I was starting, especially in a derby, and it gave me that extra buzz.
"The lads were buzzing to come away with the win against Sunderland. I think the way we performed and were able to control the game after they went down to ten men was really pleasing."
