United, who lacked any fluency at the Stadium of Light, were fortunate to take a 17th-minute lead through Juan Mata.
However, they failed to take advantage as an unmarked Jack Rodwell headed in a first-half leveller on his home debut to earn Sunderland a point.
All eyes were again on the Dutchman after United began their campaign with a 2-1 home defeat to Swansea City last week.
As if to add to the pressure, all three of the club's close-season signings – Luke Shaw, Ander Herrera and Marcos Rojo – were unavailable on Sunday.
Yet few would have predicted the level of disjointedness on display as United struggled badly, particularly in defence.
There were certainly signs of the nerves Van Gaal alluded to last week in his charges' display, although a botched attempt to play out from the back fortuitously led to an opening as Tom Cleverley curled over early on.
But the goal did not bring an improvement in the visitors' general play and Sunderland levelled in the 30th minute, Rodwell heading home Sebastian Larsson's corner at the front post.
United did begin to see more of the ball thereafter, although it was Sunderland who created the first half's final chance when Steven Fletcher's overhead kick went tamely wide.
Whatever Van Gaal said to his players at the interval did not have the desired effect as further poor defending let in Wickham, who saw his fizzing strike turned cleared off the line by Tyler Blackett.
Van Gaal's men then enjoyed a spell of pressure and were denied a penalty when Ashley Young went down under a challenge from former United defender Wes Brown.
