Pogba was punished for handball in the area and a penalty was awarded to the Hammers.
Michail Antonio stepped up to give his side the lead with the last kick of the first half.
United levelled in the second half through Mason Greenwood and now need a point against Leicester City on Sunday, to qualify for the Champions League.
Speaking after the game, when Solskjaer was asked about the Pogba incident, he said: “It’s a natural reaction.
“Paul held hands up knowing he should have taken it in the mush. It came flying at him at 100 miles an hour.”
The Red Devils have not secured a top-four finish since 2018.
