Dylan Stephenson broke the deadlock for the young Magpies inside the opening half hour in front of 1,447 spectators at Woodhorn Lane, a new ground record for the Northern Premier League Division One East side, before Jay Turner-Cooke's excellent free-kick doubled the visitors' advantage.
Despite Dan Maguire's strike swiftly reducing the deficit, United's second-string battled courageously in the closing stages against the Colliers to book their place in the final, where they will face Blyth Town at St. James' Park on Tuesday, 14th May.
"We're really pleased to reach the final," Dawson told newcastleunited.com. "We haven't won the competition for quite a while so it was one of the objectives we'd set out at the start of the season to make sure we gave a good account of ourselves in the games, with a lot of attention and fans at them and there was also a clear aim to make sure we got to the final and gave ourselves a chance to play at St. James' Park again.
"I thought we coped with the conditions really well. We knew it was going to be tough and the crowd would be up for it, with it being their last home game of the season. We factored all that in and I thought we stood up to the challenge really well.
"Ashington had a couple of good chances early on which they didn't take and we were a little bit fortunate from but we found a way to stay in the game, getting ourselves ahead and even when they scored, we have some big players who know how to handle pressure."
Newcastle's youngsters, who have won the competition a record 38 times, will be aiming to lift the trophy for the first time since 2018.
Dawson, who oversaw the young Magpies' 3-1 win against Morpeth Town six years ago, is hopeful his side can conclude their 2023/24 campaign with a piece of silverware when facing Blyth Town, who won the Northern League Division Two title this term, at St. James' Park.
He added: "I was fortunate to be around the last time we won. There's a number of Academy staff who were around or who have been here as players when they were younger and have a Senior Cup medal.
"It's something that would be great for the lads, after a long and tough season, to show for their efforts so we'll regroup, recover and look forward to play at St. James' Park.
"One of the beauties of this competition is that carrot at the end of it to play at the stadium with a decent crowd in. We've only had the opportunity to play there once this year which was on Monday night (against Aston Villa Under-21s).
"We didn't get the right result that night (a 1-0 defeat) but, hopefully, we can look forward and prepare for Blyth Town."