The young Magpies, who qualified for the last 16 prior to their away clash at Guiseley's Nethermoor Park, were unable to seal top spot in Group H, with Ryan Edmondson breaking the deadlock in the first-half.
Leeds' lead lasted for barely one minute as Jamie Sterry quickly levelled, with the equaliser involving Liam Gibson, Elias Sørensen and Sterry, who were all granted permission to participate in the cup tie despite completing January loan deals.
Edmondson added his second moments into the second half before Pascal Struijk's strike gave Newcastle a mountain to climb, as the Magpies eventually suffered their first loss in five matches. However, Dawson felt the result was harsh on his young side, who he insisted had created enough opportunities to progress as Group H winners.
"There were really good bits that we did well but also there were also some scrappy goals," Dawson told nufc.co.uk. "We had made a lot of changes to our team and then it was Leeds' cup final. We tried to stress to the lads that we weren't there just to get a draw or roll over and let them win, we were there to get the victory and try to build some momentum ahead of Friday (against Fulham).
"I thought we created some great chances and could have taken the lead. There were some good examples of pressing from the front and forcing them just to boot the ball, picking up the seconds and allowing us to play from there.
"I thought we could have been better on the break in terms of hitting areas to get us up the pitch and put our opponents under pressure. It was one of those nights where it could have went either way.
"I think the scoreline did flatter them a bit but we move on to Friday. The result hasn't cost us anything and we are through in the competition. It's now about making sure we recover correctly and get ourselves ready for the next game."
Dawson's side reached the quarter-finals of the Premier League Cup last year and the coach believes reaching another knockout stage of a cup competition will be important for his developing squad, who also enjoyed an impressive run to the Checkatrade Trophy last 16 earlier this term.
With a Northumberland Senior Cup final place also at stake, with a semi-final against Morpeth Town next month, and United currently occupying the Division Two play-off spots in Premier League 2, there will be many tournaments for the youngsters to focus on during the latter stages of an exciting campaign.
"It's important that we now put together a comprehensive games programme," Dawson added. "Getting into the latter stages of cup competitions is good and gives us an opportunity to hopefully play somebody different. It also means the lads have got something to keep ahold of and keep them going throughout the season.
"We have qualified in the Premier League Cup and are in a great position in the league. We have the Senior Cup to come next week so there's still plenty for us to aim for as a team. When you have got that insight, it spurs individuals on and keeps competition high in the squad."
