The Lancastrians prevailed 4-1 on penalties with Billy Sharp and the returning Jay McEveley missing from the spot and the Blades bowed out at this stage of the competition for the fourth time in five seasons.
The game ended 0-0 in normal time, with the Blades, who handed outings to James Wallace, McEveley and Terry Kennedy, unable to find a way past home goalkeeper Chris Maxwell.
Adkins said: “It was frustrating as we wanted to go through. We have good chances.
“It was a windy night for both sides, but we created chances and the goalkeeper has made really good saves again.
“We had opportunities to put the ball in the back of the net and have not done that.”
The main positive on the night was seeing the likes of James Wallace, McEveley and Kennedy return to the fray, with Wallace featuring for 71 minutes on his return to action while McEveley and Kennedy played the entireity of the game.
Adkins, whose side return to League One business and host Southend on Saturday, added: “I made a lot of changes, but we have a squad of players and players returning and it’s important that they are getting game-time.
“That is what we need, competition for places. We need that competition for the run of games we have got and we have got to give ourselves a chance in the league and the FA Cup.
Specifically on midfield man Wallace, he added: “You could see he has good abuility, but he’s got to play consistent football.”