Dan N'Lundulu's close range header gave Southampton a first-half lead before Tyreke Johnson nodded home the Saints' second early in the second half at St. Mary's Stadium.
Captain Owen Bailey gave Newcastle hope with a first-time strike in the latter stages of the clash but, despite pressing heavily for a late equaliser, it was not enough as Newcastle missed out on promotion to the top tier of Premier League 2.
Dawson told nufc.co.uk: "I didn't think there was much in the game. It was a little bit disappointing in the first half, conceding a poor goal at a poor time. They had a couple of half-chances as well as ourselves and I thought going into the break at nil-nil would have been a get out of jail free card.
"As much as we didn't look under threat, we hadn't started well enough and played with the intensity and urgency required. We tried to mention a few things at half-time and, after coming out (for the second half), it's another set play that has ended up costing us but this time from our own.
"From that point on, it seemed to give us a kick up the backside that we needed, playing with more tempo and moving the ball faster. Ultimately, we left ourselves too much to do in a short space of time.
"We got one back and we had Southampton penned back in. We had a great shout for what looked like a handball, with the player going down holding his head. It was a big call to make especially when it happened in injury time.
"It shows the character, togetherness and resilience of the group to keep fighting and give everything they could. Ultimately, this week hasn't been enough in the two finals but it has shown the strides that this group and individuals have made in the last nine months."
After losing in the Premier League Cup final against Everton, the play-off final defeat brought a tough end to an already impressive campaign for Newcastle's youngsters, who had finished fourth in division two on 40 points, the most gained by their Academy squad for a decade.
However, despite falling at the final hurdle on two successive occasions, Dawson said the squad have made excellent progression this term and have plenty to be proud of after notably achieving a strong list of achievements over the course of their 41-game season.
Dawson added: "It will be difficult for them to think about. They will not think back to July when we began the season and look back at the improvements they've made. They'll just remember it as getting beaten in two finals against Everton and Southampton.
"We can see on a day-to-day basis the improvements they have made as a team. They have gained the most points a Newcastle reserve team has achieved in ten years and finished the league as top scorers, finishing three behind Arsenal across both divisions.
"We reached the last 16 of the Checkatrade Trophy and were only the second under-21 team to win all three group games, since they were invited to participate, and made nine clean sheets in 41 games.
"There is a lot to be positive about and think back on. They'll be the things that we will reiterate to the group and be hoping to replicate next year.
"We're looking at the steps many have made from under-18 level last year where they played 20 games, if they've played every match, to this year playing 41. There is a third more of matches to play and the competition level goes up a few notches. There are a lot of young lads who have stepped up and I think they have worked well alongside the more senior ones that we have."