The fault lay with flawed management information and poor communication with applicants and staff which meant that senior management had no idea of how badly things were going wrong until it was too late to do anything about it.
G4S continued to give false reassurances, based on poor-quality data, to Locog, the Home Office and other partners involved in the operation until a very late stage in the process, the MPs' report said.
"Far from being able to stage two games on two continents at the same time, as they recklessly boasted, G4S could not even stage one," said Keith Vaz, chair of the committee.
"The largest security company in the world, providing a contract to their biggest UK client, turned years of carefully laid preparations into an eleventh hour fiasco.
"Because of the swift actions of the MoD, Home Office and Locog, London enjoyed a safe and secure games.
"The taxpayer must not pay for G4S's mistakes. G4S should waive its £57m management fee and also compensate its staff and prospective staff who it treated in a cavalier fashion. Their decision not to bid for Rio 2016 is the right one."
The group of cross-party MPs also said armed forces personnel should be considered as possible security providers for future major events from the outset, rather than just a backup, with appropriate recognition and reward for the personnel concerned.
Sky's defence and security editor Sam Kiley said "defence chiefs will do what they are told", but "they will not want to have to plan for the intervention of the military for domestic events except in a dire emergency".
He added: "There is a precedent for the army to step in to keep the emergency services functioning during industrial strife. Soldiers have been put on standby to keep Britain's fuel tankers running too.
"This is, defence sources say, the 'proper use' of the armed forces. 'The strategic interests of the country are our interests', they say.
"It is difficult to see how an army of what will be 82,000 by 2020 which will relying heavily on 30,000 reservists who have not yet been recruited, would be able to deliver the sort of event security envisioned by the Home Affairs Select Committee."
Other recommendations from the MPs include:
:: The company should make one-off payments to applicants who were trained up but did not get work because of G4S's own management failings.
:: The Government should keep an up-to-date central register of high-risk companies who have failed in the delivery of public services, so that they can be ruled out for further major contracts.
G4S accepted they made mistakes and apologised for their "serious failings". The company insisted the £57m 'management fee' was not profit and only covered real costs, such as wages, property and IT expenditure.
In a statement responding to the MPs' report, G4S said: "The Board and management of G4S have taken responsibility for the inability of the company to deliver, in full, on the Olympic security contract and apologise for this failure.
" ...Everyone connected with the company is extremely disappointed that G4S was unable to deliver on its full commitments on this contract, but this does not reflect the high standards G4S delivers continuously in its other work for the UK Government every day."
Findings of a review into what went wrong will be announced within the next 10 days, it added.
More From Sky News