Moyes has already shelled out £27.5million on Marouane Fellaini and £37.1million on Juan Mata since taking the reins at Old Trafford from Sir Alex Ferguson.
However, Tuesday night's 3-0 defeat by rivals City marked the sixth time this season that the reigning champions have been turned over at home in the Premier League.
They have also slipped 15 points behind Manuel Pellegrini's title chasers in the table but former Red Devils star Scholes, a guest pundit on Sky Sports' Football Special, is of the opinion that United must back their manager.
"You have to," said Scholes. "He's only nine months into the job. You have to stand by him.
"OK, he's made a couple of signings that haven't quite worked out yet, as he would have liked.
"In the summer, he's going to need backing - there's no doubt about that. Was he backed as well as he could have been last summer? I'm not too sure. But this summer, he has to be backed - and I think he knows he needs players."
Many United fans have long been crying out for midfield additions to the squad but Scholes says there are several departments of concern.
"It looks to me like there's a few areas that need addressing," he added.
"You could say that they've been looking for a central midfielder for quite a few years now, and maybe haven't quite come up with the answer.
"But it's defensively as well. (Nemanja) Vidic is going, it looks like Rio (Ferdinand) and maybe (Patrice) Evra are going as well so that's three of your back four. That's another area he's got to look after.
"I think going forward we're alright, with the quality of (Robin) van Persie, and Wayne Rooney, and (Juan) Mata in his right position. I think we're alright up there, so it's probably midfield and defence where we need to look."
United still have a Champions League quarter-final against Bayern Munich to play, but Graeme Souness says that is unlikely to put any gloss on their troubled campaign.
"This season, it's obviously down to the Champions League," said Souness.
"They're going to play the team that many regard as the best around, so that's not going to be easy.
"The Manchester United supporters will not be happy, understandably so. And I think they're going to have to be very patient, because I don't see this as a quick fix.
"I don't think, when you're talking about putting it right, you can talk about it in terms of month or years.
"I think you have to talk transfer windows. Because with every transfer window, you're not going to get the players you ideally want.
"You might have to wait six months or a year to get the ones you want. So for me this is not a quick fix here, and these supporters are going to have to accept that."
United look increasingly unlikely to qualify for Europe's elite competition next season, but Souness believes they should still be able to attract top players, though some of their targets will turn them down.
"You can put United in a group of maybe half a dozen clubs that are uniquely special," added the former Liverpool star.
"In terms of finance, they don't have to be in the Champions League to go out and buy the very best players. The transfer fees and the salary will not be an issue.
"Playing for United but not being in the Champions League might be an issue for some players - but this is a unique club."