The Frenchman had his powerful spot-kick saved by Rui Patricio as United were held to a 1-1 draw at Molineux, with Ruben Neves’ wonder-strike cancelling out Anthony Martial’s opener.
The decision for Pogba to take the kick was controversial, given that Marcus Rashford scored from the spot in the 4-0 thumping of Chelsea last weekend.
Rashford has scored every penalty he has ever taken in senior football, while Pogba has missed four of his 11 penalties in a United shirt.
Afterwards, Solskjaer moved to clarify the situation, insisting he lets his players decide for themselves who should take responsibility.
"The two of them are designated the penalty shooters and it's up to them there and then who feels 'this is mine',” Solskjaer told Sky Sports.
"Sometimes players just feel they are confident enough to score - Paul has scored so many penalties for us and today Rui Patricio made a good save.
"The two of them have been very confident. I like players with confidence and the feeling that 'I can do this'."