The young Magpies fell behind on the hour mark at the Madejski Stadium after Teddy Howe's header before Cal Roberts equalised with a fierce first-time finish, completing a splendid attacking move from the away side.
Jordan Holsgrove regained Reading's lead in the second half of extra-time before Kelland Watts' penalty in the 121st minute sent the game towards a shoot-out, with United goalkeeper Nathan Harker saving three spot-kicks along with successful conversions from Owen Bailey, Mo Sangare and Jamie Sterry resulting in a 3-2 triumph on penalties.
Dawson told nufc.co.uk: "I thought we deserved something out of normal time and extra time and certainly didn't think we deserved to lose the game. I was really pleased with the way we started the game and had large spells in the first half where I thought we were on top.
"We got into some good areas and created great opportunities that we didn't take. You're always running the risk of them getting up the other end and getting a chance which proved to be the case in the second half.
"We found a way to get back into the game and made some changes. We scored a great goal and, although it was disappointing to concede the second goal, we were given a lifeline right at the end. It was great composure from Kell (Watts) and once we got to that stage (the shoot-out), it's a lottery.
"For a lot of the group, having the previous experience of penalty shoot-outs in the last couple of seasons is important. We had the win against Sunderland in the International Cup two seasons ago and the Macclesfield victory this season (in the Checkatrade Trophy). The lads have got experience in those situations and none more so than Nathan (Harker).
"The message was that Nathan would get us one and everybody needs to do their job. As it happens, he got us more than one but the others still had to do their job and that's where the practice throughout the season came in useful so I'm really pleased."
United now face an away clash against Southampton in the Division Two play-off final along with a Premier League Cup final clash against Swansea City or Everton in the same week.
After a eye-catching season from the youngsters, Dawson believes Newcastle's second-string will be firmly focused in their attempts to gain promotion to Premier League 2's top tier as well as winning a maiden Premier League Cup to end their campaign on a high.
"We know it will be tough," Dawson added. "We knew the game against Reading would be difficult. We now need to play Southampton away in the play-off final and then we are playing in the Premier League Cup final against a team in the division above away from home. We will need everyone who is fit and available, even those who didn't get on tonight or weren't in the squad.
"Giving what's at stake, as much as they'll be tired, I think everybody be switched on and willing to give everything this week in training and in the upcoming games. I think they'll be keen to at least have something tangible to show for what has been a great season for them all as a group so far."
