Soon after the financial crisis of 2008, at a meeting in the United States, a senior economic adviser at the White House put a question to me: "Do you think banks can be good citizens?" As I started to answer yes, he interjected: "If your answer is yes, think about the fact that no one will believe you." His comment gave me pause; I've thought a lot about what he said over the last three years.

The environment in which we are all living and working is challenging. In Europe, the UK and the US, we are now feeling the effects of unsustainable levels of public and private debt. Spending cuts are being put in place by governments and households alike, with varying degrees of public acceptance and social unrest.

The single most important thing for banks and other businesses to focus on immediately is creating jobs and economic growth. To play their role, banks have to rebuild the trust that has been decimated by the events of the last three years. That requires us to use the lessons learned from the crisis to become better and more effective citizens. Put simply, the private sector has an obligation to become the engine of growth and job creation, and banks have a vital role to play in that.

Frankly, though, banks have done a very poor job of explaining how we contribute to society. We need to fix that as part of the process of restoring trust in what we do. At the simplest level, banks are entrusted with deposits from individuals, businesses and governments. We put that money to work by, for instance, helping people to buy homes or lending to growing businesses.

Banks also provide critical services to governments and business by providing direct access to global buyers of debt and equity and by establishing large, consistent markets of buyers and sellers. Some characterise these activities as speculative trading. They aren't; they serve a fundamental client need, so it's wrong when they are caricatured as gambling.

Of course, to meet these client needs banks must be safer and stronger than prior to the crises. The reality is that much is different in today's financial sector. Banks are not borrowing as much, they have more capital, and they have far more stable and liquid sources of funds to lend. Strong banks want strong regulation, and we believe that no taxpayer money should ever again be put at risk to rescue a failed or failing bank.

But three years on from 2008, we still face considerable challenges, as the continuing eurozone crisis demonstrates. So it's not surprising that many people doubt that anything has really changed.

The only way that banks will win back the public's trust is to become better citizens. That starts with how we behave, and in demonstrating we act with trust and integrity. At banks this means the interests of customers and clients must be at the very heart of every decision made.

In 1970, Milton Friedman – one of my favourite economists – wrote an influential article saying that the only social purpose of business is to increase its profits. On that point, I disagree with him. Businesses must increase profits in a way that creates sustainable shareholder value, not just short-term gain. This applies across industries, not just in banking. Look at the paths that companies like Unilever, PepsiCo and Nestlé are forging.

Banks can and should do the same by focusing on the interests of the customers, clients and communities that they serve. The challenge is balancing our obligations to all our stakeholders, both customers and shareholders, including the pension funds that help millions of people around the world save for their retirement.

That is not always easy, and the decisions that we make every day – just like any other business – are imbued with inherent dilemmas. But we have to confront those on the basis that doing what's right for customers, clients, shareholders and communities will ensure that we get those judgments right much more often than we get them wrong.

That's why I think the answer to the question posed to me three years ago is that banks must be good citizens. I appreciate that believing this will require you to see a visible difference in the way we participate in society. You may not recognise that right now. It's the early stages. We're determined to keep working at it, and I am committed to making it happen.

This article is an extract from the inaugural BBC Today Business Lecture