Troops were drafted in at the Games after the private company was unable to provide enough security guards, causing culture Secretary Jeremy Hunt to "think again" about the default use of private contractors.
And Defence Secretary Philip Hammond said only the state could provide "large-scale" contingency back-up.
G4S had a £284m contract to provide 10,400 staff for Olympic events but could not supply enough personnel, leaving some 4,700 members of the armed forces to stand in. The firm described its failures as a "humiliating shambles" and was forced to apologise.
On Monday G4S said it had donated £2.5m to the armed forces, with Mr Hammond saying the donation would "go some way" to recognising the extra work placed on the military.
Some 18,000 service personnel provided support at London 2012, including Army, Royal Navy and Royal Air Force staff, some of whom had their leave postponed.
Labour say the problems demonstrate the dangers of outsourcing security to the private sector and all future private tenders for back-office policing functions should be put on hold.
Asked what lessons he drew from the G4S contract, Mr Hunt told 5 liveBreakfast that it must be remembered that while there had been serious failures in the firm's management, many thousands of their staff had turned up for work and done a great job.
"I think we have to have an open mind," he said. "We will all look at the performance of G4S in this situation and it does make you think again about the use of private companies in certain situations."
a senior Royal Air Force officer has suggested the armed forces could take two years to recover from the extra deployment for the Olympics.
"You can't expect them [the armed forces] to go back to normal routine very easily," Wing Commander Peter Daulby told the Guardian.
The MoD said its contribution to the Olympics was planned to avoid an impact on current operations and "while some individual training and leave may need to be rescheduled, this will be managed and will not impact on operations including the ongoing mission in Afghanistan".
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