Callum McFadzean's goal early in the second half was enough to separate the sides in their League One play-off semi-final first leg and Morgan feels that is all he could ask from his players.
"We're happy because we did set out to win the game," Morgan told Sky Sports. "We knew that was going to be important in front of our own supporters and we've done that.
"In the bigger context of it, it's half time and we know that. We've done half a job tonight and we go down to Yeovil full of confidence that we can finish the job off."
The Blades and the Glovers each had claims for penalties in a nervy affair but none were given and both teams had to settle for a 1-0 scoreline.
Asked if he felt the appeals evened themselves out, Morgan added: "Yes, I think they do. It's little ricochets when the ball's bouncing around and it's hard for referees to give."
The second leg takes place at Huish Park on Monday with the winner to face either Swindon or Brentford at Wembley.