Emery’s side are without an away Premier League win since the opening weekend of the season after failing to rise to the challenge posed by fired up United at Bramall Lane.
French forward Mousset, making his first Premier League start for United, punished poor Arsenal defending in the first half to score his second goal since signing from Bournemouth.
That was enough to send Arsenal crashing to just their second defeat of the season, ending an eight-game unbeaten run in all competitions.
The north Londoners sit fifth in the league after a powder-puff performance that showed Emery’s rebuilding job is still a work in progress.
But Emery insisted Arsenal deserved at least a draw and criticised the failure to give a penalty for a foul on Sokratis.
“We didn’t deserve to lose. We can speak about two key moments, one is the goal and the other is a clear penalty with Sokratis. With VAR, the foul should have been reviewed, but we have to accept it,” Emery said after Arsenal’s winless run in the city of Sheffield extended to 26 years.
“We had more chances than them. If we scored one goal then we could have controlled better.”
Asked if Arsenal have a mental block in away games, Emery said: “We prepare for the matches the same home and away and think to win.
“We deserved more but they are a very strong defensive team.”
Under Emery, Arsenal have kept just two clean sheets in 24 away league matches and once again they wilted too easily in a hostile environment.
“We conceded a lot of corners in the first half and they scored the goal. It can happen. Above all, we have to improve by not allowing balls like that,” Emery said.
“We are playing some young players who are taking experience but the most important thing is to win.”
This was a signature win for the Blades after last season’s promotion and they sit proudly in ninth place, just three points behind Arsenal.
With the Bramall Lane crowd in full voice, a bruising clash got off to a contentious start when Sokratis appealed in vain for a penalty after having his shirt tugged by John Egan.
Emery’s men should have taken the lead when Sead Kolasinac curled a perfect low cross towards Nicolas Pepe in the six-yard box, but the unmarked Ivory Coast winger completely miscued his shot.
– Pepe struggles –
It was the latest in a growing list of disappointing displays from Pepe, who has struggled to make an impact since his club record move from Lille in the close-season.
United made the most of that escape as Arsenal’s long-running set-piece issues resurfaced in the 30th minute.
Oliver Norwood’s corner reached Jack O’Connell at the far post and he rose above Matteo Guendouzi to head down to Mousset, who poked home from virtually on the line after Granit Xhaka failed to react to the danger.
Damningly, Arsenal have conceded 22 league goals from set plays since the start of last season, with only Watford (25) and Everton (24) allowing more.
Xhaka almost conjured an equaliser with a dipping long-range effort that Dean Henderson pushed away at full stretch.
Mesut Ozil was once again left out of the Arsenal squad and, with Pierre-Emerick Aubameyang anonymous, Emery sent on Dani Ceballos, but he shot weakly at Henderson from Bukayo Saka’s cross.
Alexandre Lacazette came on with 22 minutes left for his first appearance since suffering the ankle problem that had ruled the Arsenal striker out since the start of September.
For all their territorial dominance in the closing stages, Arsenal lacked composure in the final third.
Pepe curled just wide and Kolasinac headed over as the visitors’ frailties were laid bare.
