McFadzean, 19, a first-half replacement for the injured Barry Robson, ensured the Blades will take a slender advantage into the return leg at Huish Park on Monday after his deflected 46th-minute shot settled a tense and evenly-contested tie in front of a Bramall Lane crowd of 15,262.
But Morgan, who steered the Blades to only his second win in six games since replacing Danny Wilson as manager, warned his players "it is only half-time".
"All the young lads that have been involved with us this season have been excellent," Morgan said.
"They've picked up the challenges we set them. The squad is small this year and never has there been a better time for those young players to make an impact.
"It's pleasing because it's a massive game and do the kids grasp it or do they go under?
"All the kids when I've asked them to do it have gone in and played like men and you look at them tonight and they are men."
McFadzean made his 11th appearance for the Blades during a season that has also seen the likes of fellow teenagers Joe Ironside and Elliott Whitehouse - both second-half substitutes - make the first-team breakthrough.
"We've involved them all year. They've been in the first-team squad all season and they've come on since playing with the experienced players.
"Those lads are only first year pros, they're young lads, but they've grasped the challenge and it's nice for Callum to get his first goal in front of the kop in such an important game."