Robin van Persie hit the woodwork twice, including from the penalty spot, as the visitors missed a host of chances, but the Spanish side's coach feels the result was fair
The point represents Sociedad's first of their Group A campaign, and keeps their hopes of reaching the Champions League last 16 narrowly alive after Shakhtar Donetsk and Bayer Leverkusen also played out a goalless draw.
Arrasate's side had to survive plenty of pressure from United in the second half and they rode their luck as Robin van Persie missed a penalty, but the 35-year-old felt they deserved their point.
"I congratulated my players," he told reporters. "They are on their knees after putting in a huge effort.
"When the team gives its all like that, you can only salute them.
"The point will help us to strengthen but we would have preferred to have played a little better."
Sociedad must win their remaining games with Bayer Leverkusen and Shakhtar Donetsk handsomely and hope both lose to United in order to reach the last 16.