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", and he said: 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."
He added: "All the young lads that have been involved with us this season have been excellent. 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."
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.
Morgan, who confirmed Robson had gone to hospital for treatment on a rib injury sustained in the 30th minute, said he was happy to settle for a one-goal advantage.
"We had a gameplan and I thought we were excellent," he added. "We were up against a good Yeovil team. Two good teams. The four teams that are in the play-offs are all good teams so it's going to be close. But we're looking forward to the challenge now on Monday."
Yeovil posed enough of a threat throughout to give manager Gary Johnson hope for the return leg. Sam Foley forced a superb save from Blades goalkeeper George Long, Paddy Madden's goalbound header was cleared by home defender Neill Collins and the visitors had a strong penalty appeal for handball off team-mate Harry Maguire.
"We needed to get the ball down and play and we did that when they scored their goal," Johnson said. "If we can be a bit better and take our chances on Monday, like we didn't quite today, then of course we're still well in it.
"Me and the boys feel Monday can't come round quick enough."
- Sports & Recreation
- Barry Robson