A Department for Transport spokesman said: "Stagecoach is an experienced bidder and fully aware of the rules of franchise competitions".
Stagecoach now operates East Midlands Trains.
'Passengers will benefit from the provision of free wifi throughout the franchise, both on-trains and at stations, and a significant uplift to the current ticketing system, with the introduction of smart, flexible ticketing options, including to provide better value for those who travel regularly but less than 5 days a week, as well as improved ticket-buying facilities and nine newly staffed stations.
Martin Griffiths, Stagecoach Group chief executive, said he was shocked at the DfT rejection of its bid, adding he was requesting a meeting with the DfT.
The fact that East Midlands Trains and Greater Anglia would be owned by the same operator would help with co-ordinating services, but this was something that happened between all train companies.
Refurbished trains are promised on the Liverpool to Norwich route, running via Sheffield and Manchester, but the Liverpool-Nottingham section is set to transfer early in the new franchise to another operator, which Mr Dyson expects will be TransPennine Express.
When asked about the effect this will have on the RPS, a TRP spokesperson said: "We are working closely with the scheme trustees, Rail Delivery Group and the DfT to ensure the best possible outcome for pension scheme members".
It also can not pursue a joint bid for the West Coast Partnership with Virgin Group and French national state-owned railway firm SNCF.
Sir Richard wrote: "Running the railway comes with many challenges and the West Coast Main Line was struggling when we took it over, but we were determined to turn it around".
The contract is due to begin on August 18 2019, will run for at least eight years, and will be known as East Midlands Railway (EMR).
As well as the newly revamped InterCity West Coast franchise that will include High Speed 2 operation when opens, Stagecoach bids have also been discounted from the East Midlands and South East franchises.
Across the franchise, the Government says more than £17 million will be spent improving stations, and passengers have been promised more peak time seats and compensation for delays of over 15 minutes.
"I am devastated for the teams who have worked tirelessly to make Virgin Trains one of the best train companies in the United Kingdom, if not the world", said Branson.
The decision by the Department of Transport (DfT) also means that Stagecoach is barred from bidding for two other rail franchises namely South Eastern and West Coast Mainline (which would have been a joint venture with Virgin Group and France's SNCF).
It also throws into doubt the future of the twice daily direct rail link from Shrewsbury, Wellington and Telford to London, launched in a blaze of publicity in 2014.
Stagecoach had been bidding for this franchise independently. Virgin Trains has led in the industry for more than 20 years and we wanted this to continue for many more years.
"The new East Midlands Railway franchise will also introduce enhanced delay repay compensation, with passengers able to claim compensation if their train is more than 15 minutes late".