Chris Wilder acknowledged his side weren't at their best, as Bristol City left Bramall Lane with all three points.
Despite taking the lead in each half, through Billy Sharp and Scott Hogan, it was Andreas Weimann's hat-trick that won it for the Robins.
And Wilder admitted it was a frustrating day at the office, in front of a crowd in excess of 30,000.
He remarked: "It has always been about how we respond, and it always will be. We've shown previously it's a tremendous quality in my time here and we're going to have to do it again.
"It's disappointing for everybody, the day was set up, we've taken the lead twice, but conceded three really poor goals.
"Jack (O'Connell) having to come off didn't help us, the last two goals both come in his area, and all three goals we're poor on reflection.
"Enda (Stevens) slashes at a clearance for the first, then Dean (Henderson) loses it in the sun, it should be a routine save for him."
The Blades boss added: "At 2-2, what should I do? Do we go five at back and see it out, but we're in the industry to win games, unfortunately we've been caught out and lost the game, but I'd rather have that ambition in my team to try and win.
"We weren't very good first-half, we kept turning the ball over and if you keep doing that against good players they will hurt you, regardless of shape.
"We got ourselves back in it and our shape allowed us to get in front, from there we should be the only winners, but full credit to Bristol City, they deserve an enormous amount of credit."