The Red Devils were 0-2 down at half time at home, but roared back in the second half to go top of their Champions League group.
However, Scholes believes United were extremely naive defensively, and would be put to the sword by a better team.
United take on Liverpool at the weekend in the Premier League.
"I get the United excitement, that first half put me off the second half, if they were playing a better side they would have been out of sight," Scholes said post-match on BT Sport.
"They [Atalanta] had five players missing. I get the excitement, but the display was something I did not enjoy, it was worrying, it lacked unity and to me, can they go and play against against better teams like that? No.
"It was a great night but that first half was a major worry.
"For a neutral it was a great game, full of excitement and goals but I am being realistic about what is to come. I expect more from them, cannot keep conceding chances like that, playing a decent team but not world class, you cannot get too carried away."
He added: "You celebrate every win, the first half really worried me, people say I am miserable, but I looked at that game thinking about Liverpool at the weekend and playing Manchester City [on November 6]. If you play two central midfielders against them, it'll be three or four-nil and you aren't coming back.
"It was great seeing all the shooting and crosses in second half, but that first half worried me. They showed great spirit but they conceded so many chances, quality players make sure you don't win that game. Will they play that well against Liverpool, imagine Jurgen Klopp at home rubbing his hands together watching that first half.
"Atalanta had too much possession, I don't think the performance can be good when you are two down at home, I am miserable. I kept going back to that first half, which was disastrous."
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