The Reds won the league clash at the death with a Michele Fornasier effort in injury time after the Merseysiders were reduced to 10 men following the sending off of Stephen Sama.
The victory moves Joyce's side into fourth place in the table, with games in hand on the top three - runaway leaders Tottenham, Liverpool and Southampton.
"I'm obviously pleased with the win," he told MUTV. "We kept going until the end and I thought we deserved it.
"I'm disappointed we didn't capitalise and make more use of the sending off. I thought we played better against 11 men than 10. We didn't move the ball quickly enough, work hard enough and weren't creative enough.
"There were a few mistakes defensively as well. We were sloppy at times and a little bit casual getting out to people. We should have really drove the tempo of the game when they were down to 10 men."
Jeff Schlupp, who is on trial from Leicester City, caused problems for the hosts all evening in a central attacking role.
"Jeff was unlucky a couple of times not to score with his bright movement," stated Joyce.
"It's never easy for players coming in but I thought his movement and work-rate were good and he played a part in the goal at the end as well."
The Under-21s' next assignment is a trip to West Ham's Upton Park on Friday night with the action live on MUTV.