Either side of Joe Willock's goal at the end of the first half, David McGoldrick missed two chances to score.
He missed the target after good work by Ben Osborn and Enda Sevens in the seventh minute.
His 77th-minute opportunity was audacious and self-created, but clipped the crossbar from distance.
"We started really well and stopped Newcastle playing forwards and created chances which we did not take and then we got punished at the end of the half. That's been the story of the season," reflected interim manager Paul Heckingbottom
"There was no lack of effort and those 15 minutes where weren't as good we concede a header that puts us behind, Rammers (Aaron Ramsdale) makes a great save.
"When you are chasing it's a tough game. We huffed and puffed second half, threw everything at it, had a lot of the ball and we were vulnerable to counter-attacks throwing that many men forward but you've got to."
The game was the first the Blades had played in front of supporters since March 7, 2020, albeit they were all Newcastle fans.
"I really enjoyed it," said Heckingbottom.
"We pulled up at the hotel last night and there were people in the bar, it felt different.
"As we came to the ground there were people knocking about and I had a coffee watching people come in."
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