The Red Devils twice came from behind to earn a point against the Gunners at Old Trafford, with Anthony Martial cancelling out Shkodran Mustafi's opener before Jesse Lingard struck 74 seconds after Marcos Rojo's own goal inadvertently put the visitor back in front.
Mourinho had criticised his side for overcomplicated play in its 2-2 draw at Southampton last Saturday and questioned the commitment of some of his squad.
The 55-year-old found no fault with the effort of his makeshift starting line-up, which included first Premier League starts of the season for Diogo Dalot and Marcos Rojo, but he suggested there is a limit to what he can coax out of his side by way of quality.
"Yes, it's a positive sign but there are things I cannot get from them, and I cannot say much more than this, but big soul, everybody gives everything," he told BT Sport when asked about the efforts of players to play through form and fitness troubles.
"I cannot tell you much more. I prefer just to tell you I am happy with the soul, the commitment, the bravery, I'm really happy with that."
United, which started with Paul Pogba and Romelu Lukaku on the bench, fell behind when David de Gea allowed Mustafi's header to slip through his grasp and cross the line 26 minutes in.
Martial responded but it was another mistake that led to Arsenal's second goal, with Rojo conceding possession and contriving to put the ball into his own net after running back to challenge Alexandre Lacazette.
The match was reasonably end-to-end in the closing stages, but Mourinho felt that was only the case because United gifted the visitor its openings.
"Come on, [it was] open because they scored the second goal, if not it was a second half with a clear tendency of one team waiting to see if they could take a point and another team increasing the pace and the intensity," he said.
“We shoot ourselves so many times during the season that it's really difficult, 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 brave guy to play with such difficulties he had. The boys left what they had and sometimes people speak about the quality..."
When asked if United had taken on board his demands for "simplicity" after the Southampton match, he replied: "Yeah, it's true, we had that, but we should win the game.
"We make two big mistakes for their goals, other mistakes that allowed them to have counter-attack situations, easy passes that we lost, easy controls that we lost, and again our performance is marked a little bit by these ups and downs."
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