The only goal of the game came in the 21st minute when Bolton striker Gary Madine netted from close range.
“It was very frustrating,” Blades boss Chris Wilder said. “We created chances, but we were poor in finishing it off and we made poor decisions in the final third.
“It was a massive missed opportunity and a smash-and-grab victory from our opponents. There was nothing tactical about their goal. If there was then we would have conceded several times.
“We were the dominant team, but that doesn’t mean we are the better team. We need to be more ruthless in both boxes to sustain our league position.
“We had a sensible talk because we keep being a mug side. We knew how they played but it didn’t work for us today.
“They analysed how we played and were able to get in behind. All they did was whack it up to Madine and it cost us. I’d prefer my teams not to play like that.
“We defended poorly out wide. It wasn’t anything to do with them playing better. We’ve not marked well enough in the box.
“It became a scrappy game after 15 minutes but we came out well.
“We dominated the game but we lacked that quality that I believe would have won us the game. We were the better team and that last little bit was missing.”
Wilder made two changes, captain Billy Sharp back in attack in place of Clayton Donaldson, while John Fleck returned in midfielder after serving a three-match suspension.
The inclusion of former Wednesday striker Madine brought the expected jeers from the Lane supporters.
But that was all the excitement there was in the opening exchanges, as both sides tested each other out.
Mark Duffy looked most likely to cause an opening for United, and his trickery created a half-chance, and when his cross was cleared to Fleck, the midfielder volleyed wide from long distance.
But it was Madine who opened the scoring on 21 minutes, tapping home in front of the Kop, after a superb cross from Antonee Robinson.
The former Owls forward also had a big appeal for a penalty turned down following a tackle from Cameron Carter-Vickers, who was replaced by George Baldock on 31 minutes.
John Lundstram threw himself in front of Karl Henry's shot, while Fleck was booked for a crunching tackle, as United faced a spell of pressure from the visitors.
It was 37 minutes before United had their first real chance, Baldock forcing Ben Alnwick into a low save to his right.
And the Wanderers stopped came out on top again, after thwarting Leon Clarke when United's top scorer burst through on goal.
Jack O'Connell came close to a second-half equaliser, but saw his header flash wide, while Alnwick diverted Baldock's low shot beyond his left-hand post.
Clarke missed a glorious chance to grab a late equaliser, firing wide from close range, before substitute Samir Carruthers drilled a low shot wide.