Since January — a month before the club entered bankruptcy protection because of its tax debts — "close to 21 players" have departed Ibrox to leave the squad desperately short of personnel, according to McCoist.
The Glasgow-based team, which has won a record 54 domestic league titles, was barred this week from competing in the Scottish Premier League and will discover on July 13 which of the country's three lower leagues it will be entered into for next season.
"We have (the threat of) a transfer embargo hanging over us but how can I operate with a transfer embargo when I only have six players? It's impossible and it's just madness," McCoist said.
"I have in the region of six first-team players at preseason training right now, two of whom were regulars last season in the SPL. We need to bring in the region of 10, 12 or even 14 players ... We have to start rebuilding and replacing."
Failure to secure agreement with British tax authorities led to a consortium purchasing the club's assets last month in a 5.5 million pound ($8.6 million) deal and establishing a new company.
The repercussions of Rangers' financial problems have been huge, with the club relegated from the SPL, banned from European football for three years and losing many of its best players, among other sanctions.
"There is no-one more angry, disappointed, embarrassed and apologetic than me," McCoist said. "This should not have happened to our football club."
McCoist, a former Rangers and Scotland striker, met with a fans' group on Wednesday and said the majority of supporters want the team to start from scratch in the third division, Scotland's fourth tier.
The decision rests in the hands of the 30 clubs in the three lower leagues.
"Whatever decision they reach, we will accept," McCoist said.