Nigel Clough felt the Blades were worthy winners at Villa Park on Saturday.
Goals from Scottish duo Jamie Murphy and Ryan Flynn paved the way for United to cause the shock of round three to date with a deserved 2-1 success and afterwards the Gaffer heaped praise on the players.
A jubilant Clough remarked: "We thoroughly deserved the victory and the manner of the win pleases me as much as the result itself.
"We were fortunate on the stroke of half-time when Christian (Benteke) missed with two headers, but I honestly thought overall we had the better of the chances.
"The first goal was perhaps slightly fortunate with the deflection, as was Villa's equaliser with how the ball broke, but there was nothing lucky about the winner.
"We knew to win this tie we needed everyone to a man to be at their best and work their socks off and they did.
"It is even more remarkable when you consider that those lads have played the majority of five games in the space of two weeks."
The manager added: "Paul (Lambert) put out a strong side and we had a sneaky feeling that would be the case.
"He had been honest in the week and said the Premier League was Villa's priority and I understood his comments.
"But he certainly didn't want to lose the game that is for sure and he was visibly bitterly disappointed to have been knocked out of the FA Cup at the end of the game."