Not all parts of the financial system need fixing, Lord Turner said.
"Radical change" is needed in the financial sector in order to restore public trust, according to the head of the City watchdog.
Banks must focus on their "essential social and economic functions", the Financial Services Authority (FSA) head Lord Turner said on Tuesday night.
He also told the BBC the FSA had got regulations on the amount of money banks keep in reserve "quite wrong".
Excessive risk taking by banks was seen as a factor in the economic downturn.
Banks must focus on restoring the public's trust in their role, despite signs of economic improvement, Lord Turner said.
He argued that the industry should consider carefully any business that fell outside its core roles, saying that bank bosses should walk away from activities that had no "social benefit".
Lord Turner told the BBC that banks should "rededicate and commit themselves" to their traditional role of deposit-taking and lending to individuals and businesses.
He said they "had fooled themselves into thinking that continual innovation of [complex] products was a good thing", whereas in fact they did little but create confusion and instability.
Banks traded these products "with far too small slices of capital" to protect against losses.
But rebuilding trust would not mean an end to well-paid traders "much as some might like it", Lord Turner said.
Lord Digby Jones, former head of employers' group CBI, told the BBC that criticising bankers was not helpful in the current economic climate.
"Financial services is about 10% of GDP, about 17% of personal taxation revenue and about 23% of business taxation revenue," he said.
"If this nation is going to reduce its debt and keep paying doctors, nurses and teachers, we need a financial services industry and smacking bankers is not the way to go about it."
"Bank investments might become more boring, but after the last year, there's a lot to be said for boring," Lord Turner said in a speech to the annual Lord Mayor's City Banquet on Tuesday.
He said one of the biggest challenges for bankers was to regain public trust and to rebuild an understanding that banks and financial markets provided "not only socially useful, but vital functions".
Lord Turner said the City of London still had plenty to offer and that many parts of the financial system "aren't bust and don't need fixing".
However, he added: "It is possible to say that, but also recognise that, not all financial innovation is valuable, not all trading activity plays a useful role and that a bigger financial system is not necessarily a better one."
Much of the ire about the crisis in the banking sector has been focused on the pay and bonuses received by some bankers.
Lord Turner said it was possible to "overstate the importance" of the role banker bonuses had played in the crisis.
But he acknowledged it was an area for legitimate public concern.
The FSA's main response to the crisis has been demanding that banks build up greater buffers of reserves and liquidity so they can cope with any future difficulties.
And Lord Turner said the banks' focus should be building up reserves, ahead of paying out hefty remuneration.
He said that at the G20 meeting in Pittsburgh, leaders would seek to get global agreement on the priority for how bank profits were spent.
It would be easier for banks to moderate bonus payouts if they knew that competitors were doing the same, he added.
"An industry that recognises the need to moderate excesses, rebuild trust and embrace reforms to prevent another crisis will prosper," Lord Turner said.
"The real enemies of the City's success and of the market economy, with all its great potential to spread prosperity and opportunity, are not those who raise these issues, but those who want to ignore them."
French President Nicolas Sarkozy has led the charge to install mandatory caps on bonuses which the UK and US have opposed.