United, who started with Paul Pogba and Romelu Lukaku on the bench, showed great spirit to twice come back, with equalisers from Anthony Martial and Jesse Lingard earning a much-needed point.
But, after a defeat at Manchester City and dispiriting draws with Crystal Palace and Southampton, United are now 18 points behind leaders City and actually closer to the relegation positions than they are first place.
United also trail Chelsea and Arsenal, who are now unbeaten in 20 games, by eight points in the battle for a place in the top four.
And Mourinho, who saw a bad David de Gea error and Marcos Rojo own goal twice hand Arsenal the lead, believes the performance continued their run of self-inflicted harm.
"We scored four goals and we drew 2-2," joked Mourinho.
Mourinho's frustration was especially understandable given that Arsenal's opening goal, after 26 minutes, featured that rarest of collector's items, a mistake by his Spanish international goalkeeper David de Gea.
Chris Smalling slipped at Lucas Torreira's 26th minute corner, allowing Mustafi the space to send a free header bouncing into the ground and goalwards.
It looked a routine save for United's number one but he succeeded only in pushing the ball into the air, two-handed, over his own head and over the goalline, despite Ander Herrera's desperation clearance.
But United responded within four minutes as Rojo, playing for the first time this season, unleashed a terrific free-kick which Bernd Leno kept out at the foot of his left-hand post.
Herrera responded quickly, although replays suggested he may have been fractionally offside, reaching the loose ball on the by-line and turning it into the six-yard area where Martial was able to convert.
That dramatic pattern would be repeated after 68 minutes when Arsenal regained a lead they could only hold, on this occasion, for 74 seconds.
Lacazette played a one-two with fellow substitute Henrikh Mkhitaryan and advanced into the area where Rojo tackled him from behind and succeeded only in turning the ball into his own net.
But there could be no faulting United's response as Arsenal panicked at a long ball punted forward, almost directly from kick-off.
Sarri slams Chelsea's complacency in defeat at Wolves
Maurizio Sarri accused his Chelsea players of over-confidence after throwing away a lead to lose 2-1 at Wolverhampton Wanderers on Wednesday.
Chelsea looked to be on course for victory thanks to Ruben Loftus-Cheek's early opener as the visitors dominated the first-half, but two goals in four second-half minutes saw Wolves secure their first win in seven games and inflict just Sarri's second defeat since taking charge in the summer.
Next up Chelsea face the daunting task of halting Manchester City at Stamford Bridge on Saturday and Sarri suggested a jolt to their confidence could be a blessing, but declared himself "worried" by the manner of their defeat at Molineux.
"After this match we are less confident but maybe it's better because sometimes my players show me that they have too much confidence," said the Italian."I don't know why. I am really very worried, not for the result but the fact that after the first goal we conceded we did not react very well. I am really very worried for this, not for the result."
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