The Gunners could have climbed back to third in the Premier League table but Lys Mousset’s first-half goal earned the Blades all three points.
Emery is under pressure to deliver a return to the Champions League but the team’s mixed start to the campaign has a number of supporters on edge.
#EmeryOut trended on Twitter as Arsenal fell to defeat at Bramall Lane.
And a host of fans demanded the Spaniard’s sacking as soon as the final whistle sounded.
“Our luck finally ran out. Sack emery tonight idc anymore I’m done,” one furious fan said.
“EMERY OUT! ALLEGRI IN!” a second said.
“Can we please just sack Emery now,” a third demanded.
“Get him gone,” added a fourth.
Another simply said: “Sack him.”
Referencing the lack of Mesut Ozil in the match-day squad, this fan said: “Could have done with Ozil’s creativity in the final third but no. Thanks Emery. Get out of our club.”
Another moaned: “This is inexcusable. No substance to what we’re doing. No logic to leaving ozil our. No belief in his players to beat a promoted team. Put us out of our misery. Freddie or Arteta til the seasons over.”
One supporter joked: “Good ebening. We are now 1 game nearer to Emery’s goodbye.”
While another wrote: “No one to blame but Emery. He had far better players available today but picks his favourites again.”
Emery moaned after the final whistle that Arsenal did not deserve to lose.
“When we were losing 1-0, we controlled the game but and defended well but they had a lot of players in their box so it was difficult to achieve attacks,” he said.
“We created three or four chances and we spoke about scoring one goal, we could have controlled it better if we did.
“We have challenges in each match. Tonight we had a big challenge to get the three points.
“We are playing some young players who are taking experience but the most important thing is to win.
“The result is one thing, but we can analyse positively.”
Jubilant Sheffield United boss Chris Wilder said: “To host a game like this, the magnitude, to play like that and get the win.
“We limited them to few chances and backed up a good performance with a good result. We did not get that a few weeks ago against the European champions but three points is a great reward for the players.
“It is absolutely crazy that we can open up against Arsenal. We saw their ability, skipping round our challenges so we had to balance it in and out of possession.
“Getting ahead gave us something to hang on to. Dean Henderson made a couple of saves but it has tipped from the Liverpool game where we should have got something and tonight we did and we deserved it.”