Scholes has been keen to point out what a setback losing former chief exec Gill at the same time as Sir Alex Ferguson was to his former club.
He told BBC Radio Five Live: "When you look five or six years ago when Sir Alex Ferguson left, the only person that's probably going to get the credit he deserved was David Gill.
"He was a football man. From the day he went, as well as Sir Alex, it's been difficult.
"I think there were alarm bells straightaway really when David [Moyes] took over and he signed Juan Mata and Fellaini for something like £70m.
"They're good players in their own right, but I don't think they were Manchester United players.
"I don't think Sir Alex or David Gill would have signed those types of players, so I think from then on, alarm bells have rang and we're in the position we are now because of buying players who we don't really think are Man Utd players.
"Ole's come in and he's got the opportunity to put that right."