Morgan, who made nearly 300 appearances for the Blades as a player before joining Danny Wilson's backroom staff, was handed the reins when the former Northern Ireland international left Bramall Lane in midweek.
Speaking after goals from Chris Porter and Dave Kitson put Swindon to the sword, Morgan said: "If we are going to get promoted then it's going to be through team unity and that's what we had out there.
"Every professional footballer is talented but if you've got that desire and determination to be better than your opponent then that's going to stand you in good stead. That's what we had out there."
Morgan added: "That's an important win for us but I guarantee you there won't be two happier people seeing that result than Danny Wilson and (his assistant) Frank Barlow.
"It's never nice when people leave because there are people here, myself included, who have a great affinity with Danny and Frank. But the response was excellent."
- Sports & Recreation