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 but insisted his side must cut out their silly errors.
Asked what he said to the players at half-time, United boss Solskjaer told BT Sport after the match: "I said make sure we get the next goal - if we do we win the game. As long as we don't concede again, we will win the game.
"We created lots of chances in the first half, it was just about taking them. I thought we played well in the first-half. They had two chances and scored two goals - which has to stop.
"We have a habit of doing that at this club. Out of nothing they scored and then scored from a set play. But we never stopped believing and kept going. We made a few mistakes, but we kept going."