United's second-string trailed at half-time in their final Group F fixture at the Impact Arena following Manni Norkett's opener before the visitors responded brightly after the restart, netting twice in the space of three minutes following Alex Murphy's header and Amadou Diallo's penalty.
Although Newcastle's youngsters are unable to progress into the knockout stages of the Premier League Cup, Dawson expressed his delight to end their participation in the competition with maximum points, the young Magpies' first away win of the 2023/24 campaign in the process.
Dawson told nufc.co.uk: "It's been a long season already with a lot of games and times where we've performed well and not got the result we've deserved but I thought, tonight, we deserved the result.
"It wasn't the result we wanted in terms of trying to progress but, nonetheless, it was still nice to get the win to go with the performance.
"We hit the woodwork after five minutes and you think if that goes in, it builds momentum for us and then they go and score a poor goal from our point of view in terms of defending the corner better but the lads stuck to the plan really well and controlled large parts of the first half.
"We tweaked a few things at half-time, making a couple of changes and it was a really bright start to the second half which then builds confidence again and allowed us to get a good foothold in the game.
"We show signs of good control in games but we need to do slightly better in terms of keeping the ball out of the net but some of that comes with taking our chances at the other end.
"We create opportunities but if you don't take them at this level, there's always a risk it goes in at the other end. If we take those opportunities earlier, it takes the pressure off the backline and the team defensively so it goes hand in hand."
Alex Murphy completed a commendable performance for United's second-string, completing his first full game since August following a hamstring injury with a maiden goal for Newcastle at under-21 level.
The Irish defender, who made his Premier League bow in November during the Magpies' 4-1 win against Chelsea at St. James' Park, also produced an emotional signal to the sky after netting against Forest following the passing of his grandmother on Sunday.
"It was nice to see Alex get through 90 minutes," Dawson added. "It's been a long time since he got a hamstring injury from the Manchester City game in September and he's since been training with the first-team and involved in matchdays.
"We have been fortunate he's come back and played some minutes for the under-21s. It was good to see him on the pitch for the full game and putting in a really good performance along with that.
"It can sometimes be difficult when you haven't played a full game for a long time but he coped with it really well and the goal was a nice touch for him at this moment in time."
