The young Magpies host their Terriers counterparts at Whitley Park on Wednesday evening (kick-off 7pm GMT), aiming to move level with their upcoming visitors at the top of Group G on six points.
White, who made his Magpies first-team debut during a pre-season friendly at Rotherham United in July, is keen to end a run of four consecutive games without a win to enhance United's chances of progressing into the last 16 of the competition.
"It's a big game," the 19-year-old midfielder told nufc.co.uk. "We had a disappointing result in the first game (a 2-0 loss against Watford) and then bounced back against Birmingham (winning 4-0). I think, especially when you get to the new year and you're finishing the season off, you want to be playing as many games as possible to better ourselves both as individuals and a collective.
"To get through and try to get as far as we can would be quite big for us. The group is quite tight at the minute. We're playing a team top of the group so we have to bring our A game.
"There's been a few disappointing results and performances lately. There's been positives to take but we haven't got the results so if we can take the positives into Wednesday, taking what we've learnt and what we can get better at, then hopefully that can lead to a good team performance and win to give us a good chance of qualifying.
"The team got beat off Everton (in the final) a few years ago and we want to try and get to the final again and better that by winning the competition."
The young Magpies suffered a heavy 6-3 defeat at Mansfield Town in the Papa John's Trophy group stages, despite leading twice in the Northern Group H encounter.
White has recorded six assists so far this term but expressed his delight in registering his first goal at second-string level, completing a wonderful solo finish against the Stags, and now has his sights set on adding to his maiden goal with United's under-23 side.
White, who has represented England at under-18 level, added: "I think relieved is the best word to describe it! I've waited a long time to score.
"I've had a lot of assists this season and the Sunderland one where my shot hit off Jay's (Turner-Cooke) back and went in summed my luck up in front of goal! To finally score, in the way I did, was a good feeling.
"Numbers are really important in terms of where I play on the pitch. My assist tally is good for this season so hopefully the goals can start coming now.
"Scoring three times against a Football League side was good and the goals being of high quality was even better. There's quite a few from the team that may want to go on loan so those types of games give us confidence to show what we can do against senior opposition."
Supporters will be able to attend Wednesday's Premier League Cup clash at Whitley Park, with season ticket holders gaining free admission otherwise it's £3 for adults and £1 concessions.
