In a speech to students and financial industry figures at the London School of Economics, Stephen Hester rejected the view that a company's sole objective was to make profits and attacked the "scandal" of poor customer service.
The head of the part-nationalised Edinburgh institution, which he described as a "poster child for what went wrong in banking", said banking customer care had fallen behind that offered by supermarkets and said financial institutions must be aware of their impact on society.
Mr Hester, who was forced to waive his near-£1 million bonus, called for banks to become better servants to customers and said that since the 1980s "the definition of corporate success became dangerously narrowed".
Following a similar call by Lloyds Banking Group chief Antonio Horta-Osorio to CBI Scotland in Glasgow for the banking model to be "recast", Mr Hester added: "To paraphrase Milton Friedman, 'the social responsibility of a company was to increase its profits'.
"That became the prevailing view and critics would argue it remained that way for banks right up until the 2008 crash.
"Evidence points to a different and more balanced conclusion now."
Mr Hester, who was hired to replace Fred Goodwin after RBS's £45 billion Government bailout in 2008, said: "Hubris set in. Too much of the ethos became selfish – personally and institutionally."
"Ask any member of [supermarket] staff for the most obscure item and they will stop what they are doing and take me to the item immediately. Banks have not kept the same pace in either service or product.
"It is possible to look at the many scandals that have hit banking in recent years and see them as individual episodes of bad judgment or wrong behaviours. In fact, I think it's more accurate to say that most of them are related to one big scandal: Banks have simply not been good enough servants of their customers in the recent past."
Barclays has been fined £260m by regulators for attempts to manipulate the key London Interbank Offered Rate, or Libor.
RBS is under investigation by global authorities for its role in the scandal, and billions of pounds have been set aside by the industry to compensate customers mis-sold payment protection insurance.
Mr Hester said: "We have to address the root cause of the industry's failings. And that, for me, is very clearly the need for better focus on serving the customer well in our collective cultural DNA."
After Mr Horta-Osorio had said the focus on sales targets had contributed to mis- selling in retail banking, Mr Hester said: "If you want good people, you have to first engage their heart and their head before their wallet."
Which? executive director Richard Lloyd has called for "a return to banks for customers, not bankers".
Colin Borland, of the Federation of Small Businesses, said: "If customer focus is now going to be at the heart of it, then I look forward to seeing what that entails."
Liz Cameron, chief executive of the Scottish Chambers of Commerce, added: "A return to focusing on the needs of the business and personal customer is well overdue."
l Police are investigating RBS over allegations it engineered the takeover of the Coniston hotel in Sittingbourne, Kent, from its own borrowers, to establish whether a crime was committed.