Arsenal came close to winning the game on several occasions but De Gea made up for his error with some fine saves.
Whatever troubles have befallen United they can usually rely on Spanish keeper David de Gea but even he seemed to suffer with the "panic" Mourinho says can overcome his side.
Manchester United have been struggling to find consistent form this season under the Portuguese coach and there is likely to be plenty of speculation as the January transfer window draws nearer.
Mourinho said: "They played well".
United had an answer in the 31st as Leno palmed a Marcos Rojo free kick toward the end line but Herrera kept it in bounds with an industrious effort that went right to Martial.
A harmless corner from the visitors turned out to be United's undoing, Smalling out-muscled by Mustafi who fired a header towards De Gea.
Inside Nick Jonas and Priyanka Chopra's Traditional Hindu Wedding
In the lead-up to their twin ceremonies, Chopra and Jonas hosted several events that blended both of their backgrounds. The couple's Hindu wedding took place on the palace grounds, with Mehrangarh Fort as the backdrop.
The Red Devils, on the other hand, have managed just one Premier League win in four games. Watching on ahead of the game tonight two of the regular pundits, Rio Ferdinand and Paul Scholes, were unsure of whether Mourinho deserved to get the sack if United get beaten by Arsenal tonight.
His only concern was a nasty-looking ankle injury sustained by Joe Gomez in the first half.
What is the big team news for both sides?
Tottenham have 33 points, six behind Liverpool, and two more than Chelsea and Arsenal.
"We shoot ourselves so many times during the season that it's really hard, but fantastic attitude, many players in difficulties, some good performances but players in difficulty, Diogo Dalot first start, Marcos Rojo first minutes, Matteo Darmian first start, Eric Bailly doesn't play for a couple of months, Chris Smalling a courageous guy to play with such difficulties he had".
This time the lead lasted a matter of seconds as United replied with Lingard sliding the ball under Leno after a lapse in concentration by Sead Kolasinac.
Southampton, Burnley and Fulham occupy the three relegation spots with nine points each.