The Robins had started the afternoon one place above the Blades in the table but the two teams looked worlds apart as goals from John Brayford, Ryan Flynn and a Jose Baxter penalty eased the host's relegation worries, dumping City back in the bottom four.
"I was surprised and, unfortunately, the scoreline was a fair reflection of what went on," said Cotterill. "I can't dress that up at all and it's very difficult to talk about what happened to be honest.
"We were abysmal. We didn't do anything. Certainly nothing that we'd shown in training during the week.
"We showed no composure when we needed it and too much composure when we didn't.
"I'm a winner and I don't like it when my teams down't win. But I like it even less when they play like that."
"We had a great following here and we let them down badly. Sheffield United have not sprung any surprises on us whatsoever out there. That makes it even harder to take.
"This is a great football club and it's painful when you see things like that happen to the team. What we've got to do is dust ourselves down and then, in our next game, look to put that right.
"I try and be a positive person but, to be honest, there are very few positives, if any, that I can take from that."