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.
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.