The Red Devils struggled for fluency throughout against Marco Silva's side and the result could have been worse for them if a superb effort from Lazar Markovic late on had not caught the post.
United's best chance fell to Juan Mata, who appeared certain to score at the far post when Chris Smalling headed across goal only for Eldin Jakupovic to make a stunning save.
Chelsea, Tottenham, Arsenal and Liverpool all failed to win in their respective league outings on Tuesday but with Manchester City beating West Ham, Jose Mourinho's men remain adrift in the race for Champions League qualification.
Mourinho opted to start Marcus Rashford on the left despite Anthony Martial's impressive performance in the FA Cup, with Wayne Rooney then introduced from the bench at half-time.
The England captain failed to make much of an impact, however, leaving United winless in three Premier League matches.
After a disjointed opening, United began to exert control in the 15th minute – their purpose signified by Zlatan Ibrahimovic's 25-yard drive, which was tipped around the post by Jakupovic.
They then crafted another opportunity from the resulting corner, but Marcos Rojo headed over after Henrikh Mkhitaryan's delivery was brilliantly flicked back into the danger zone by Rashford.
United's dominance in possession showed no sign of letting up and Hull spent prolonged periods camped in their own area.
But the hosts did not create another chance until the 35th minute, with Pogba teeing up Ibrahimovic on the edge of the area for what was ultimately a scuffed left-footed effort straight to Jakupovic.
The goalkeeper was given significantly more of a test just before the break but again he denied United, as Pogba latched on to Ibrahimovic's clever backheel and saw his left-footed strike pushed away.
Jose Mourinho looked to add extra invention to United's attack by replacing Michael Carrick with Rooney at the start of the second period.
But it was Pogba who inspired their next chance 10 minutes later with a long ball over the Hull defence to pick out Rashford, who could only scuff wide despite a marvellous first touch.
Rashford was involved again shortly after, heading Antonio Valencia's cross into the danger zone only for Ibrahimovic to half-volley just wide from eight yards after Rooney completely missed the ball.
United should have gone in front 16 minutes from time but again Jakupovic came to Hull's rescue, denying substitute Mata from point-blank range after Smalling headed a corner across the face of goal.
In the end it was Hull who went closest, with only the post preventing Markovic from making an already frustrating outing even worse for Mourinho after the end of a swift break.