The Red Devils were staring down the barrel of a fifth loss in eight matches and were booed by some fans as they trudged off at half-time trailing by two goals, only for Solskjaer's side to storm back memorably at Old Trafford.
Marcus Rashford struck on his first start since the Europa League final and Harry Maguire lashed home a leveller, setting up a box-office finish that Cristiano Ronaldo delivered with a powerful header from Luke Shaw's cross.
However, United's defensive frailties were once again clear for all to see and despite their comeback, Scholes reckons they could be in for a hiding at Old Trafford this weekend when they face Liverpool.
Speaking on BT Sport, he said: "I don't want to sound like a party pooper because it is a great night for the fans, Ronaldo is the hero again, winning us the game. But that first half is a major worry for me.
"It looked anything but a team. It just lacked unity.
"Can they go and play against Liverpool like that? Never in a million years."
Solskjaer praised his side for 'always believing' in the clash and told others not to 'disrespect the players'.
He said: "The fans are a big part of this club. The singing section there kept the players going with their belief. That is what you do at Manchester United on a Champions League night.
"I thought we played well first half too. Two chances, two goals. It had to stop if we are to survive. We have a habit of doing this at this club.
"I thought we played well and they scored a goal out of nothing and then another set-piece. But they never stopped believing and kept going.
"Don't disrespect the players. They play for Manchester United and they know they are the luckiest men in the world. Tonight they are the luckiest men in the world because they get to play for Manchester United. That is what so many millions of boys and girls want to do.
"Rashford had chances in the first half but Marcus kept on going. He got a knock but he is going to be very important for us.
"It was instinctive finish from Harry. I don't think you would have expected him to score that one.
"And Cristiano is great in front of goal. If anyone wants to criticise him for effort and work-rate just watch this game. Watch how he runs around.
"At half-time, I said make sure we get the next goal, because then we win the game. As long as we don't concede I was pretty sure we would win the game.
"It was just about taking chances."