Javier Hernandez missed the first real chance of the match five minutes after half time when he blazed over from close range.
The Dutch striker then had a chance to score from the spot when Ashley Young was adjudged to have been fouled in the area, but he hit the same upright with his penalty.
Marouane Fellaini was shown a second yellow card late on for United, eventually being given his marching orders for persistent fouls.
Here, Sports Mole takes an in-depth look at a frustrating night in San Sebastian.
On target 0
On target 2
Was the result fair?
Neither side was at their best this evening, but United will feel more aggrieved with the draw due to the chances that they created. It was by no means an all-conquering performance by the visitors, but Hernandez's miss and Van Persie's two shots that hit the post were chances that you would usually expect both to take with relative ease. In terms of general play, there was little to separate the two sides in a distinctly ordinary match, but those chances could and should have made the difference.
Real Sociedad's performance
The La Liga outfit are not a bad side, but they don't seem to have enough Champions League quality in their midst. They rarely troubled United's defence and, with the exception of a short period immediately after half time, it was the visitors who looked more like the home side. They needed a win tonight to stand any realistic chance of progressing through to the knockout rounds, but they simply didn't show the level of urgency that usually accompanies such knowledge. They will be happy with a point against a team of United's calibre, but in truth they rode their luck a little considering the chances that the Red Devils passed up.
Manchester United's performance
It wasn't a vintage United display by any means. They just about edged an uneventful first half without creating much in attack, while they also had the best of the second half when the match began to liven up around the hour mark. However, their general play was slow and predictable, and it was only when Robin van Persie and Ashley Young came on that they started to threaten regularly. On another day, they could have won 3-0 with Hernandez and Van Persie missing gilt-edged chances, but that would have been a deceiving scoreline. An away point in Spain isn't a bad result, but they will have to play a lot better when they come up against the bigger teams in the tournament.
Sports Mole's man of the match
Shinji Kagawa: There wasn't exactly a plethora of candidates for this award, but Kagawa gets it for being the most dangerous player on the pitch during the uneventful spells. He came closest for United in the first half with a couple of efforts from the edge of the box, while he also did really well to set up that golden chance for Hernandez five minutes after the restart. Van Persie deserves a mention as he changed the game more than anybody, but his two misses rule him out of serious contention.
There is only one winner here. Javier Hernandez makes his living off being a penalty-box predator, so when Kagawa's pass fell to him six yards from goal with the keeper out of the question, everybody in the ground expected the net to ripple. Incredibly, however, the Mexican lifted his shot high over the crossbar when it appeared easier to score. It did take a small bobble, which no doubt helped the elevation of the shot, but a player of Hernandez's standing should be finishing them with his eyes closed.
Nicola Rizzoli had a good game overall, keeping firm control over the match. He perhaps awarded a few too many fouls, but most of his decisions were correct and he didn't accompany the large number of free kicks with too many cards. His decision to send Fellaini off in the closing stages did seem a little harsh, but he made it clear that it was a totting up offence against the Belgian.
Real Sociedad: Things don't get any easier for Sociedad as they travel to the Bernabeu to take on the mighty Real Madrid on Sunday.
Manchester United: United also have a big domestic clash as they welcome league leaders Arsenal to Old Trafford on Sunday.