Travis Binnion heaped praise on United's youngsters as the Blades secured a berth in the last 16 of the FA Youth Cup on Monday night.
For the third time in four ties, United were victorious on penalties after coming from 2-0 down to draw 2-2 after extra-time against Millwall at the New Den.
Jake Eyre gave United hope in the second-half, before Ben Whiteman restored parity from the penalty spot and after a nervy extra 30 minutes for both teams, midfielder Louis Reed netted the winning spot-kick to seal an 8-7 sudden-death victory.
Speaking afterwards, U18s coach Binnion was understandably delighted: "It was a very spirited performance, yet again. We showed great character to bounce back from trailing 2-0 and overall we fully deserved to win the game.
"Everyone played their part on another memorable night; the comeback demonstrated a real togetherness which is something we pride ourselves on.
"Even when we came in at half-time two goals behind there was still that belief and desire within the group and ultimately the players got their reward.
"Millwall were far better than us in the first-half and deserved their advantage, but we dusted ourselves down and were excellent in the second period."
Looking ahead to a home last 16 clash with Everton, Binnion added: "We move on to the next round and that will be an excellent tie for our lads at Bramall Lane, against top-flight opposition.
"I'm sure our fans will get down to support the lads and let me say the players really deserve the backing."