The Black Cats were trailing 1-0 until the 84th minute and heading out of the Checkatrade Trophy until a late rally saw Sunderland through.
The Under-23 side – boosted by five first-teamers including Seb Larsson and Vito Mannone – levelled through sub Josh Maja before a 90th-minute Haydn Hollis own goal sealed victory in the final group game.
“I think we deserved to go through on the night," said Stockdale to the Sunderland Echo.
“They were a constant threat with Alan Smith up top, and our two young centre-backs were great against someone who's strong and physical.
“That's something that you can't replicate in training and development squad games, so, from our point of view, it's a fantastic experience.
“It felt a bit like a knockout game. I know we could have gone through with the draw.
“But when you're 1-0 down with 10 minutes to go, or whatever it was, it feels like a knockout and the players were experienced enough to do what they needed to do.
“They got over the line in the end. I don't really doubt the character of the players in the academy. Its one thing we instill in the players, you just keep going and I think you see that from all of the teams I've had.
“It's not so much what we put into them, that's the players job.
“But, ultimately, at 1-0 if we go 2-0 down, that's really difficult to claw back. We rode our luck, Vito [Mannone] made a couple of important saves for us and ultimately two bits of quality win us the game."