Dean booked young Gunner Bukayo Saka in the incident, despite Blades defender John Egan appearing to make contact with the winger.
He then proceeded to issue a yellow card to Arsenal assistant manager Freddie Ljungberg for his protestations.
Arsenal fans also believed they were denied a spot-kick when Sokratis had his shirt tugged from a set-piece.
“Such a blatant penalty! Mike dean is centre of attention again,” ranted one fan.
“Shame mike dean wasn’t so eagle eyed to spot the blatant shirt pull on Sokratis,” added another.
A third had the same view: “Blatant pull of the shirt in the box – not even reviewed and Mike Dean just looks at it and carries on.”
Prior to kick-off Sky cameras had captured the official looking wide-eye while collecting the match ball.
And Arsenal fans jokingly claimed that the 51-year-old is actual a cyborg and not a human being.
“Mike Dean is definitely some sort of Cyborg!” claimed an infuriated Gooner.
“I don’t mind refs making genuine mistakes, just admit it and apologise…simple.”
Another Gooner gave up hope, tweeting: “I don’t expect a single decision to go our way with mike dean reffing. May as well just unplug The VAR machine now.”
Former Celtic striker Chris Sutton reckoned Arsenal showed a lack of fight at Bramall Lane after Lys Mousset gave Sheffield United the lead.
He wrote on the BBC match blog: “I never like to criticise players for… I don’t think it’s a lack of effort, I just think Sheffield United have been more committed.
“Arsenal know what’s coming, they know Sheffield United will be in their faces. You have to match that and from there you can start playing, maybe they’ll do it in the second half but by then it could be too late.”