Newcastle fell behind through Sam Osborne's first-half strike and Elliot Ward's emphatic volley from distance, giving County a considerable lead at Ilkeston's New Manor Ground.
However, United produced a resilient fightback as Mo Sangare replied with a first-time finish to set up a tense finale before Kelland Watts, who started on the bench, produced a looping header two minutes from time which was enough to send the Magpies top of Group G.
After conceding their second goal on the hour mark, Newcastle dominated the latter stages of the match but, despite another comeback from the under-23s - their fourth in the last six matches - Bailey was disappointed that his side were unable to take home three points.
"I think we all know it's a game we should win," Bailey told nufc.co.uk. "No disrespect to our opponents but I think we played the better football and we were probably the better side but we need to really show it and, ultimately, I think coming away with a point is a disappointing result even though we were two goals down.
"I was pleased with the team's fightback and showing good character to come from behind to get a point. It's not the first time that we've done that this season.
"There have been a few games where we've went behind and been able to come back and go on to draw and win games but I think it's quite frustrating that when we've dominated, particularly in the last half hour, we've scored twice but it wasn't enough to get the win."
The skipper, celebrating his 20th birthday, almost marked the occasion with a goal, with his long range strike flashing inches wide of the post.
Then, in the dying stages, Bailey provided a defence-splitting pass into the path of United's Tom Allan but the teenager was unable to find the winner, opting to unselfishly square the ball into the path of Yannick Touré with the overhit pass unable to find the forward.
Bailey added: "It was disappointing not to get the victory, especially on my birthday! It would have been nice to grab a birthday goal but, to be honest, the result is far more important.
"Everyone has had chances throughout the game and we all know the whole team have to be better, not just one or two players. We created enough chances to win the game but we need to convert them and we need to create a bit more than what we did.
"We have a lot of momentum coming from behind and although we couldn't score a third, it is a good achievement to come from two goals down which we can use to our advantage against Wolves, where we need to try and win to help our position in the play-offs.
"In the (Northumberland) Senior Cup, we are looking to win the trophy again (after lifting it in 2018), which will be hard as Blyth Spartans are one of the best teams in the competition but, hopefully, we can get two positive results and carry on from where we left off today."
Photo credit: Dan Westwell