The local government secretary's candid comments came as he said the government would be judged by voters on its record in fixing Britain's creaking rail network.
'I think the third way has been tested in the cauldron. I think those principles are still valid,' he said.
'However, it has meant some of the softer edges of the third way have been shown to be flaky.
'I do believe there are some areas where the private sector can add value, but I also believe there are areas where the private sector has tried and failed.'
Mr Byers added: 'There is not a love affair with the private sector.'
Dave Prentis, general secretary of the largest public sector union, Unison, said the majority of the public now saw the private sector's shortcomings.
'Where the third way has meant embracing the private sector as the answer to improving public services, it has been more like the failed way,' he said.
'I believe it's more than flaky. I believe we are getting through to the public that the private sector does not necessarily represent value for money.'
Mr Prentis maintained his union wanted 'world-class public services'.
'We want reform based on the real needs of the public services, not an ideological preference for the private sector,' he added.