The National Audit Office (NAO) disclosed that 12 priority investors sold all or some of their holdings within the first few weeks of trading.
Critics of the privatisation said the spending watchdog offered "startling proof" the Government sold off the country's family silver "on the cheap".
However, Business Secretary Vince Cable said the report showed the Government achieved what it set out to do - securing the future of the universal delivery service through a successful sale.
The NAO said Mr Cable's department took a "cautious" approach to a number of issues that led to shares being priced at a level "substantially below" the initial trading price.
On the first day of trading last year, Royal Mail's shares closed at 455p, 38% higher than their price sale, representing a first day increase in value of £750 million for the new shareholders.
Amyas Morse, head of the National Audit Office, said: "The Department was very keen to achieve its objective of selling Royal Mail, and was successful in getting the company listed on the FTSE 100. Its approach, however, was marked by deep caution, the price of which was borne by the taxpayer.
"The Government retained 30% of the company. It could have retained even more and allowed the taxpayer to participate further in the rapidly increasing share price and thus limit the cost of to the taxpayer of its cautious approach."
The Government could have retained 110m more shares, worth £363m, at the offer price, while still privatising the business, said the report. The NAO revealed that six priority investors sold all their shares within weeks of trading, while a further six sold part of their holdings, and four others increased their holdings.
The 16 priority investors were allocated shares worth £728m worth of shares, while another 94 institutions were given shares worth £570m.
The government of Singapore and the Children's Investment Fund Management each have over 3% of total shares, but other priority investors have not been named.
Those that sold their shares made a "substantial" profit, said the report.
Mr Cable said: "We secured the future of the universal postal service through a successful sale of a majority stake in Royal Mail, predominantly to responsible long term investors. Achieving the highest price possible at any cost and whatever the risk was never the aim of the sale.
"The NAO confirms we have protected taxpayers from the risk of needing to offer continuing support to the company as well as safeguarding the vital six day a week service that customers and businesses around the country rely on."
Shadow business secretary Chuka Umunna said: "This report delivers a damning verdict on the Tory-led Government's botched Royal Mail fire sale, leaving the taxpayer disgracefully short-changed by hundreds of millions of pounds. At the same time, stamp prices have shot up 30% and vital services have been put at risk at a time when families are already being hit by a cost-of-living crisis.
"We now know definitively that far better value for taxpayers could have been possible had ministers adopted a different timetable for the sale. The NAO could not be clearer: the inflexible timetable set by ministers for Royal Mail's privatisation resulted in the public losing out."