Boss Roy Keane was again left bemoaning individual defensive errors after his side came within a couple of injury time minutes of recording their first league win of the season.
Keane said: "It should have been three points. We were close but not close enough. At 3-1 up we should have seen the game out but we conceded some bad goals. We gave the ball away cheaply and gave it away.
"It was disappointing but we'll look at the positives. The team expressed themselves and we played well, showing a spirit and tenacity.
"It's hard to take because in our predicament it's wins you need, not draws. But the signals are that we're making progress. Perhaps we just need a bit of luck and the rub of the green.
"Our supporters were excellent again and hopefully they can see a spirit, desire and attitude among the players that says we're all in it together.
"Does it feel like a defeat? Probably not because we've scored three goals away from home but there was a spell in the second half where we were wanting one or two players to see the game through but nobody did tonight. It's very disappointing."
Sheffield United assistant manager Sam Ellis was delighted to grab the draw: "We won't get a better point all season. To not play well and be second best all night shows the character of the team and that's what got us the point here."