In a statement, the company said it "deeply regrets" the problems which have meant 3,500 troops being drafted in at the 11th hour to make up a shortfall in security guards.
"G4S accepts its responsibility for the additional cost of the increased military deployment resulting from the shortfall in workforce delivery," the statement said.
"The company is also incurring other significant costs as it endeavours to meet the contract challenges.
"Whilst it is not possible to gauge the precise financial impact, it is estimated that the company will incur a loss on the contract in the range of £35 million to £50 million, all of which will fall in the current financial year."
G4S chief executive Nick Buckles expressed regret that the firm had been unable to meet its commitment to the London Olympic Organising Committee (Locog) to provide security guards.
"We are deeply disappointed that we have not been able to fully deliver against our contract with Locog and that it has been necessary to call upon the additional military personnel," he said.
In its statement, G4S said it had run into difficulties in processing applicants in sufficient numbers through the necessary training, vetting and accreditation procedures in what it described as "an extremely complex workforce supply contract" on an "unprecedented scale".
"As a result, we will be unable to deliver all of the necessary workforce numbers," it said.
"We have worked very closely with Locog throughout the build up. At the point we felt that we could no longer assure the scale of the security workforce we had committed to, we advised them of the situation."
Yesterday David Cameron said that firms who failed to deliver on their contracts to the games should have to bear the cost.
"I'm absolutely clear that if companies don't deliver on their contract then they should be pursued for that money," the Prime Minister said.
G4S was initially contracted by organiser Locog in 2010 to provide 2,000 security staff for £86 million, but that figure has since risen to 10,400 personnel in a contract now worth £284 million.
Asked earlier week whether there would be any financial penalties for G4S on its £284 million contract, Home Secretary Theresa May said the firm's deal was with Locog, but she understood that penalty clauses were included.
Mr Buckles has now been summoned to appear before the Commons Home Affairs Committee on Tuesday to explain to MPs what had gone wrong.
The chairman of the Commons Public Accounts Committee Margaret Hodge said they would also be summoning G4S, Locog, the Home Office and the Department for Culture, Media and Sport to give evidence when Parliament returns in September.
She said it was imperative that there was "total transparency" when public money was involved.
"What the National Audit Office has said to me is that it is unlikely that we will be able to clawback for the taxpayer money spent on overheads - that is where the big money has gone," she told BBC Radio 4's PM programme.
"What none of us know is how that contract was designed, whether there was a penalty clause in it. Clearly we have to pursue that point.
"Where public money is being used, hiding behind commercial confidentiality is simply not good enough."
A total of 17,000 servicemen and women will now be involved in the Olympics, including 11,800 soldiers, 2,600 sailors and marines, and 2,600 airmen.
Some 11,000 of these will be involved in the security of more than 30 sporting venues and some 70 non-competition venues, including car parks and hotels, while others will carry out specialist support roles including air security, search teams, communications and logistics.
Overall, a 23,700-strong security force for the Games will include a mix of military, private security guards and at least 3,000 unpaid London 2012 volunteers.
Students applying for jobs with G4S last year were as young as 17 as they would still have reached the minimum age of 18 by the start of this month, messages on internet forum The Student Room showed.
One wrote last August: "I passed the interview. No experience in security or anything and they signed me up for X-ray scanner.
"They claimed I would get a job if I passed the clearing phase, which takes up to 3 months ... typical British efficiency hahaha."
Another added: "It's all a bit intimidating beforehand, but as soon as you get there all the interviewers are barely 25, really nice and sympathetic. I had no exp. either."
Other posts suggested the interviews involved simple sight and smell tests, a document check and questions about when the applicant resolved a conflict and what actions were taken.