The decision of Pogba to take the penalty was criticised post-match after teammate Marcus Rashford had dispatched one so clinically last week against Chelsea .
Solskjaer claimed after the match that the decision was down to the players and not him, prompting Sutton to give him both barrels on BBC Radio 5 Live .
“It is the job of the manager to designate,” Sutton said. “That is a huge moment. United could have won the game.
“You can’t say ‘I’ll leave it down to the players’. I like Ole but that’s weak management tonight.
“Rashford may have missed as well but we’d have understood because he took the last one.
“He shouldn’t be allowed to make that decision himself. It wouldn’t be allowed under someone like Sir Alex Ferguson.”
United had led the match through Anthony Martial’s first-half goal, before Ruben Neves levelled with a superb curling effort which cannoned in off the crossbar.
But the Red Devils had the chance to restore their lead, when Pogba was felled in the box by Connor Coady, only for Patricio to thwart the Frenchman’s effort.
When quizzed after the match on why Rashford didn’t take the spot kick, Solskjaer said: “The two of them are designated penalty takers.
“It is up to them who take it there and then.
“Sometimes players feel like they are confident to score. Today Patricio made a good save.
“You can see the slide on the powerpoint that this is the plan.
“We won’t change it after this week. The two have been confident. Last week Marcus scored a goal and today Paul was confident.
“I like players with confidence.”
United legend Gary Neville also weighed in on the debate on Sky Sports, and fumed: “Pogba has missed four of them over the last 12 months, so you would think he has had his chance.
“Rashford scored last week…take the penalty! There wasn’t a leader out on the pitch. They couldn’t make a decision between them. It was embarrassing.
“Something wasn’t right.
“Initially I was fuming at Pogba as I thought ‘typically you, you selfish, why are you trying to take a penalty off a player’ but I’m holding off on it.”