The Bush administration was sharply criticised for distributing billions of dollars from last October's bailout, or Troubled Asset Relief Programme (Tarp) - which Geithner renamed the Financial Stability Plan - with few requirements on how banks would use the money and with little transparency.
Geithner said he realised there was considerable scepticism over the efficiency of the original programme, approved by US congress last October.
"The spectacle of huge amounts of taxpayer money being provided to the same institutions that helped cause the crisis, with limited transparency and oversight, added to public distrust," he said.
US stocks slumped following Geithner's remarks, with the Dow Jones Industrial share index falling 381.99 points or 4.62 per cent to 7,888.88 at the close of trading.
Geithner's speech was originally scheduled for Monday but was delayed partly so that the senate could approve the economic stimulus bill of Barack Obama, the US president.
It also came as Obama was to hold his second "town hall" meeting in Florida to discuss the latest government stimulus plan.
The senate was due to vote on it at around the same time on Tuesday.
Lawrence Summers, head of the National Economic Council, said on Sunday that the administration had received several proposals for how the private sector could be involved in the solution to the banking crisis.
"With the right strategic approaches, Geithner believes that we can bring in substantial private capital, and that's ... a better root to solving this problem than government resources," he said.