Norwich took the lead through Simon Power before United replied with two first-half goals, courtesy of a Cal Roberts penalty and Rosaire Longelo's tidy finish on the stroke of half-time.
The fixture also saw Florian Lejeune make his comeback from injury, with the French defender playing 45 minutes following a serious knee injury he sustained in pre-season.
After suffering a 2-1 defeat against City in mid-September, the Magpies have now lost once in their last 12 competitive matches as they aim to challenge for a play-off spot in the Premier League 2's second tier, lying two points adrift of fourth place Southampton, with Newcastle's youngsters facing the Saints on Friday night.
"Overall, I was very pleased with the improvements in their performance," Dawson told nufc.co.uk. "I thought we were miles better in terms of pressing higher up the pitch and creating a lot of opportunities from that.
"When we did get the ball and could not create something, we managed to control the game by overloading at the back and making some passes to find a way in playing through them.
"We made a sloppy mistake which allowed Norwich to score but we never really looked back after the goal and the two goals we've scored, especially taking the lead just before half-time, put our opponents on the back foot."
And, despite going behind, Dawson was delighted with the reaction from his side as United dealt their opponents a significant blow with two goals in the final five minutes of the first-half, with Longelo's match winner coming seconds before the break.
Dawson added: "A goal at anytime is great but scoring just before the break changes what the opposition are going to say in the dressing room and reminds us that what we're doing is working and we need to stick at it.
"As much as we had some good chances on the break, Norwich won the ball at times and managed to play through the initial press but then struggled to get through our backline without creating any clear cut opportunities.
"From a defensive point of view, it is something we are currently doing really well at and when we get set and are more compact, we seem to control the space very well."
