Pogba won the penalty, drawing a foul from Wolves captain Conor Coady, but saw his spot-kick was saved by goalkeeper Rui Patricio.
It was Pogba’s fourth miss from the spot since the start of last season. No Premier League player has missed more than him in that time.
The decision for Pogba to take the penalty was all the more questionable given Marcus Rashford’s successful spot-kick against Chelsea last weekend.
Rashford, who has never missed a penalty in his career, was chosen ahead of Pogba at Old Trafford last week but was overlooked on this occasion.
Solskjaer revealed that he does not designate a single penalty taker, instead trusting his players to step forward if they feel confident enough to score.
Appearing on Sky Sports, former United full-back Neville criticised the policy, comparing the uncertainty to a ‘tombola’.
“Tonight there was a debate between [Anthony] Martial, [Daniel] James, Rashford and Pogba,” he said. “It was more like: “Go on mate you have it”.
“This is not right, by the way. Look here comes Paul Pogba, now [Jesse] Lingard is getting involved. Is Pogba the penalty taker and Rashford has taken it off him?
“I’m holding back on Pogba because he may be the penalty taker here. It isn’t right. They should decide before they play. This is not right.
“This is a Manchester United penalty. This is not tombola. This is not five a side. Rashford throws the ball to Pogba. Something is not right.
Neville added: “Why is there a debate on who takes a penalty? Pogba has missed four in the last 12 months – so you would think he’s had his chance now. Rashford scored last week, take the penalty.
“But there wasn’t a leader on the pitch. You saw the clips there, James was there, Martial, they couldn’t make a decision between them. Something is not right there.”
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