The young Magpies fell behind in the last-eight tie at Whitley Park following Joe Ames' opener for the Northern League Division Two outfit before Amadou Diallo's penalty and Ellis Stanton's impressive header quickly swung the cup clash in United's favour.
James Huntley's spot-kick and Kyle Crossley's emphatic finish extended the hosts' lead further in the second-half as Newcastle's second-string booked a semi-final meeting away at Ashington and continued their hopes of lifting the trophy for the first time since 2018.
"The aim in any cup competition is to get through," Dawson told nufc.co.uk. "The group suffered a heavy defeat on Friday night (7-1 against Chelsea) and the good thing is there was another game around the corner for them to put things right.
"In this competition, you play against difficult opposition against men who have played the game at a high level, making it competitive, having a good organisation and shape and wanting to win just as much as we did.
"I was hoping the technical quality and physical capacity our lads have was going to be enough. We were disappointed to start the game we did, going behind, but the group have shown all year they have good character and resilience to find a way in getting back into the game and building their confidence.
"Once we got the second and third goal, it was about maintaining good habits and seeing our way through the game."
Newcastle's youngsters will travel to Woodhorn Lane to face Northern Premier League Division One East side Ashington, who compete in the eighth tier of English football, and Dawson is hopeful his side can continue their passage towards lifting the Northumberland Senior Cup title for a record 39th time.
The winner of the semi-final tie will face either Blyth Town or Newcastle Benfield in the final, which will be staged at St. James' Park.
"Any cup semi-final you get into, you want to win regardless of who it's against and where you're playing at and get through," he added. "The biggest thing the players at our club have to deal with is the level of expectation.
"From the outset, at the start of the season, it's widely accepted that our lads should win the competition or everybody thinks that. There's an expectation. I think it falls on us and the lads have to learn to deal with that pressure.
"It'll be no different in the semi-final against Ashington and an expectation from the majority of people that we have to win the game and go and show we are good enough to do that."
Newcastle's second-string turn their attention back to Premier League 2 action next week, facing away trips to Sunderland and Middlesbrough, with Dawson aiming to prevail against their North east rivals to bolster their hopes of qualification for the play-offs this term.
"Those derby matches are something that you look forward to straightaway as soon as the fixture list comes out," he said. "It's important for our lads to rest and recover well as these games demand big, physical performances because of the emotions that come with it.
"You're then hoping that your technical side of the game is enough to get your nose in front, stay in front and come out with three points. The lads will work again before next week and then we'll look forward to both of those games away from home."
