Sir Richard said he was "extremely disappointed" that the Department for Transport (DfT) had preferred Aberdeen-based FirstGroup to Virgin which had run the London to Scotland West Coast line since 1997.
Sir Richard added: "Based on the current flawed system, it is extremely unlikely that we would bid again for a franchise."
FirstGroup, which already runs a number of franchises including Great Western and ScotRail promised cheaper fares, more services and improved stations.
But Sir Richard said bankruptcy had hit former East Coast main line operators GNER and National Express who had "overbid" for the East Coast franchise.
He went on: "Sadly, the Government has chosen to take that risk with FirstGroup and we only hope they will continue to drive dramatic improvements on this line for years to come without letting everybody down."
Sir Richard added that this was the fourth time Virgin had been outbid in a franchise tender process.
He went on: "On the past three occasions, the winning operator has come nowhere close to delivering their promised plans and revenue, and has let the public and country down dramatically
"GNER and National Express over promised in order to win the franchise and spectacularly ran into financial difficulties in trying to deliver their plans. The East Coast is still in Government ownership and its service is outdated and underinvested, costing passengers and the country dearly as a result.
"Insanity is doing the same thing over and over again and expecting different results. When will the Department for Transport learn?"
FirstGroup will take over the West Coast line on December 9, with the franchise running for 13 years and four months.
The DfT said the franchise deal was worth £5.5 billion over the lifetime of the contract.
Sir Richard said Virgin had submitted "a strong and deliverable bid based on improving customers' experience, increased investment and sustained innovation".
He went on: "To have bid more would have involved dramatic cuts to customer quality and considerable fare rises which we were unwilling to entertain."
Sir Richard said Virgin had transformed the West Coast line, more than doubling annual passenger numbers and last year paying a net premium of £160 million to the taxpayer.
Announcing the new franchise winner, Rail Minister Theresa Villiers said the new franchise would deliver "big improvements for passengers, with more seats and plans for more services".
But the RMT transport union warned of "massive cuts to jobs and passenger services and huge increases in fares".
FirstGroup chief executive Tim O'Toole said the company was delighted to win the franchise.
He went on "We will be making significant improvements including reduced journey times and introducing new direct services."
The DfT said benefits of the new franchise would include:
:: Around 12,000 extra seats a day when the new 11 six-car electric trains come into service;
:: This is in addition to the 106 extra Pendolino carriages currently being introduced into operation which will deliver more than 28,000 extra daily seats;
:: More services: Initially First West Coast will operate the timetable they will inherit from the current franchise but are seeking to introduce a number of new services including a London Euston to Blackpool service from 2013 and, from 2016, services from London to Telford Central, Shrewsbury and Bolton;
:: Improved services: Journey time improvements between London and Glasgow are planned, as well as additional services from London to Preston.
:: Improved stations: First West Coast is taking over responsibility for maintenance at 17 stations and will spend at least £22 million on a station investment programme.
Mr O'Toole said: "Our winning bid is a deliverable proposition that is compelling for all who want to see a greater use of our rail networks.
"We will be making significant improvements including reduced journey times and introducing new direct services. We will improve marketing and deliver a smart ticketing system, refreshed and improved train interiors, station upgrades and even better catering.
"In support of our commitment to generate increased passenger growth we will be reducing standard anytime fares by 15% on average."
Mr O'Toole said First West Coast would continue to invest in front-line staff and looked forward to welcoming new employees.
He went on: "Our bid also delivers value for taxpayers by returning premiums to the Government underpinned by sustainable growth in passenger numbers and revenues from the utilisation of significant available capacity.
"The new franchise will provide an economic return for our shareholders and is value enhancing from day one."
RMT general secretary Bob Crow said: "FirstGroup and the Government should be left in no doubt that we will mount a massive industrial, political and public campaign to stop any attacks on our members' jobs and the services that they provide to the travelling public as a result of this franchise award.
"We are already preparing a ballot for industrial action in light of the threatened job cuts."
He added that the franchise was being let "with a gold-plated, extended contract linked to massive cuts to jobs and passenger services and huge increases in fares as the winning FirstGroup looks to extract every penny that they can in profit".
Mr Crow went on: "The new First West Coast deal in an exercise in casino franchising that lays bare the whole sordid enterprise which is rail privatisation. Companies promise the earth, jack up fares and slash jobs and services in a drive for profits and if the numbers don't stack up they throw back the keys and expect the public sector to pick up the pieces."
"FirstGroup pulled the pin on the Great Western route to dodge £800 million in payments due to the British taxpayer and here they are just months later in control of the West Coast route. The highly political award of this contract turns the UK rail industry into a global laughing stock and the British taxpayer will be rightly outraged."
Manuel Cortes, leader of the Transport Salaried Staffs Association rail union, said: "This crazy franchise lottery, where the highest bidder scoops the pot, means that passengers will have to pay inflation-busting fare rises on the busiest line in the UK for the next 14 years.
"That is the only way that FirstGroup will be able to pay their annual £500 million premium to Chancellor George Osborne as well as rewarding their shareholders with profits."
Mr Cortes went on: "We already pay the highest rail fares in Europe and this cock- eyed lottery means they will only go even higher in the future.
"We should take a leaf out of Europe's book and run a not-for-profit, publicly owned railway which benefits the passenger and not private shareholders."
Virgin Rail chief executive Tony Collins questioned the bidding process, suggested his firm's proposed franchise deal was the maximum deliverable - and First Group would not hit its targets.
He said: "We know the franchise extremely well. If we thought we could get 10% year on year growth, we would have bid that. We don't believe that is possible."
Mr Collins admitted this could be the end of Virgin Trains, adding: "I think if this is the sort of bid that is accepted, then it is not for us."
But First Group chief executive Tim O'Toole said his company had a track record of successful delivery.
He said: "I think if track record is how we are to judge this, First Group has a track record of winning deliverable bids and delivering growth of this level on its franchises."
Mr O'Toole said he was confident First's projections could be delivered because of spare capacity in the West Coast Main Line, promising thousands of extra seats and promotional campaigns to drive people to the railways.
He said: "We are projecting growth along the line of what has been achieved in the last 10 years on the railway."