De Gea failed to come for a cross that led to Leipzig's third goal in a 3-2 win.
They had gone 3-0 up at that stage, before United scored two late goals and attempted a rally to score the equalizer.
United had only needed a draw from the game to qualify for the knockout rounds.
Scholes said on BT Sport about the third goal: "De Gea, here. He bottles it, doesn't he?
"He's scared of getting himself hurt.
"It should never go across the box like that, Harry Maguire looks wooden, he's very stiff.
"De Gea, as a goalkeeper you make yourself as big as possible.
"You might get smashed in the face and you might get hurt.
"He actually makes himself smaller.
"For such an experienced goalkeeper, it's criminal."