The former 'Gers midfielder believes Neil Lennon already has a strong squad in place at Celtic Park and has urged McCoist, who is going into his first season as manager, to go after some quality players so they can continue their recent dominance.
"Ally is in at the deep end now but I just hope Rangers can give him the money he needs to strengthen the squad," Miller said.
"We have two rookie managers in charge of the Old Firm but I think Neil Lennon has the edge in terms of his team.
"He has already got a very decent team and only needs to add one or two players.
"Ally has to maybe get five good ones in as they have lost a few. It would be especially good if they could get Kyle Bartley back.
"They need to strengthen because last season, although we won the league, we struggled to get by.
"Celtic ended up gifting us the title by losing at Inverness.
"Rangers will definitely not get away with it next season. I don't think they would be as consistent.
"Last season the consistency was unbelievable which helped them win the title.
"There is a great mentality in there. They are winners.
"Rangers have been on their knees for the last three years but have still won the league each time."