The young Magpies, who kicked off their 2026/27 EFL Trophy campaign with a 3-1 comeback win at York City last week, led at the break courtesy of Matheos Ferreira's terrific curling finish at Mbanq Valley Parade.
United's youngsters, however, were pegged back against the League One leaders courtesy of Nick Powell's close-range header before the Bantams substitute's fierce drive doubled his and the hosts' tally, with the visitors reduced to ten men in stoppage-time following Johnny Emerson's red card.
"In the first half, we played some exceptional stuff and had control for large parts of the first half," Stockdale told newcastleunited.com. "We knew there'd be a reaction from Bradford.
"Graham [Alexander] had put on some of his main players because we had them rattled. You could see that with how the game finished in terms of trying to kill the game at the end.
"I've said to the boys in the dressing room that we've ran the team that are top of League One really close. It felt like a proper game and their players were doing fist pumps to the crowd at full-time. That's how we pushed them.
"It's a shame we knew they were going to be a threat from crosses and wide positions and, maybe, playing three games in seven days caught up with us but we need to play with that intensity and bite about us in the league fixtures because it's been lacking in those."
Despite the loss resulting in a "disappointed" squad which contained three 16-year-olds, Stockdale believes his youthful squad can take a lot of credit for their valiant display against the former Premier League side, with City's starting XI averaging an age of 26.
He added: "Overall, there was going to be some heat in the game during the second half because they were going to step on us and I felt we didn't deal with that, which is my only criticism.
"We got a little penned in for 10-15 minutes. That would be the only learning curve but you've got the likes of George Mair, Alfie Seldon and Jayden [Kouossu], who are all 16, and a lot of first-year pros playing which is a brilliant experience and opportunity to show what they're about.
"They contributed in a really positive way and, although we didn't get the result tonight, I think we've managed to tick a lot of boxes in terms of development and winning in a different way for us.
"That's not to say we don't want to win the game and we're really gutted we couldn't, at least, take the game to penalties."
Newcastle's youngsters, who currently occupy top spot in Northern Group C, will seal qualification for the knockout stages of the Jersey Mike's Trophy by securing maximum points against Rotherham United, which takes place at the AESSEAL New York Stadium on Tuesday 3 November [kick-off 7pm BST].
Stockdale believes the final group clash will provide a "different" test as the young Magpies aim to reach the Round of 32 stage for the first time since 2018/19.
"The good thing about these competitions is there is a prize for winning," the Redcar-born coach added. "We push to win in the Premier League 2 and the attitude has to be to win but this is knockout football now.
"We don't have loads of knockout football in our programme so when we play Rotherham, who beat York on penalties tonight, it's going to be a tight group.
"It's still in our hands and, if we play like that, it gives us a chance but the challenge is to play like that on a more regular basis and not just turn up when we're in a nice stadium in front of fans. We have to do the nitty gritty stuff, in the Newcastle United way, every time."
