Recent loan recruit Billy Paynter was disappointed to kick-off his Blades career with a defeat - especially after taking an early lead.
Paynter, who arrived at Bramall Lane on-loan until the end of the season on Friday from Doncaster Rovers, made his Blades bow as a second-half substitute at Meadow Lane and admitted United should done better, having got into the ascendancy.
The Liverpool-born striker said: "We started the first-half strongly and deserved to go in front. I said to Conor (Coady) after the game that if he had hit his second chance like he did the first he and we would have had two.
"We had Notts County on the back foot for the first 25 minutes and should have been at least two goals up, from there I think we would have won comfortably. Unfortunately they grew into the game after their equaliser and finished the first-half strongly.
"They have got some good wide players, but we didn't defend well enough and the manager was pulling his hair out that both goals came from crosses."
Paynter acknowledged that the hosts probably handled the testing playing surface slightly better than United, adding: "The surface didn't allow us to get the ball down and play, County got their tails up and it became more of a battle. They deserve credit for making it tough for us.
"Given the start we had the final result is doubly disappointing, though, because this is a game we should have won."