First half goals from Jamie Murphy and Harry Maguire gave the Blades a significant half time advantage over City, but efforts from Gary Jones and James Hanson early after the restart saw Phil Parkinson's men roar back into the contest.
Parkin was unhappy with the nature of City's defending for both of United's goals in the opening period, but he more contented with the character and spirit shown by the Bantams as they clawed their way level in the second half in front of their 3,000+ travelling supporters.
He said: "We were really disappointed with the two goals we conceded and we needed to show a response after the break.
"We didn't play particularly poorly in the first half - we created some very good chances from some set-plays - so we were very disappointed with the players to come in at the break two goals down.
"The general attitude and endeavour in the first half was really good but we have to defend better than we did for their goals.
"In fairness to the lads though, they put that right with two goals of our own and a clean sheet in the second half.
"We don't roll over and give in at this football club, and I think we've shown that again today (Saturday). We had a full staff here backing the lads, plus over 3,000 fans, so the lads knew what they had to do in the second period.
"They kept plugging away, showing a lot of heart in the process, and we deserved to get back in the game when we did.
"We were having to hang on in a little bit towards the end but I think that was because we'd put so much effort in to get back in the game.
"The lads were throwing themselves in front of shots and crosses and putting their head in where it hurt."
One of the more controversial moments in a highly-watchable contest at Bramall Lane came shortly after the hosts had taken a seventh minute lead through Murphy.
A City corner was headed onto the crossbar by Hanson before Carl McHugh's effort on the rebound was blocked on the line by United attacker Jose Baxter.
The Bantams players around the incident felt at the time that Baxter had used his arm to clear McHugh's goal-bound away, with replays of the incident seeming to suggest that City had a case.
Parkin continued: "I thought it was a handball.
"He definitely seems to move his arm up towards the ball.
"The important thing is though, despite not getting the decision, we didn't let our heads drop. The lads showed a tremendous amount of spirit throughout."
In a slight tactical tweak at the start of the second period, Matthew Bates was moved to left back to allow Carl McHugh to join Rory McArdle in central defence.
Parkin explained: "Batesy has a little bit more pace and a bit more experience, so we just felt it would be the right change to make for the second period.
"We still suffered a little bit down that left hand side in terms of the width they got with (Ryan) Flynn but, in general, we coped with the crosses and got the blocks in when we needed to.
"In fairness to Sheff United, they threw the kitchen sink at us towards the end of that second half but we stood up and held them off."
Recent signing Aaron Mclean made his City debut against Sheffield United. The striker started the match up top with James Hanson before being replaced by Andy Gray in the ninetieth minute.
Parkin said: "I thought he showed a lot of tenancy out there and produced some good touches.
"He never gave the defenders a moment's peace and he also found himself on the end of a couple of half-chances as well.
"It was his first game up front with James Hanson and at times they looked a decent threat.
"He kept going and going, and we now have eight days or so on the training ground with him to get him really up to full speed."
With next Saturday's home fixture against Port Vale rearranged due the Valiants' F.A Cup commitments, City's next match now will be against Preston North End at the Coral Windows Stadium a week on Tuesday.
Parkin added: "Normally we would want another game quite quickly, but this period gives us a little bit more time perhaps to get a couple of players in. It also gives us a little bit more time to assess where we are at the moment with the squad.
"It gives the physio department a little bit more time with the players who are injured as well, so it could be a welcome little break for us and a chance to get a good week's training under our belts."