(FORTUNE Small Business) – It is a universal law that we all make mistakes. It's what we do to make amends that separates the leaders from the losers. Unfortunately, we've recently seen many CEOs, from Martha Stewart to Merck's Ray Gilmartin, who have seemingly made serious errors in judgment but who, in the eyes of the public at least, have refused to own up to their actions. Their original sins were bad enough, but their refusal to take responsibility was worse, angering disgruntled employees, stockholders, customers, and public officials. Those executives could have salvaged some respect had they only fessed up to their problems early on.

In most cases your staff, clients, and others will forgive a miscalculation, a case of undisciplined exuberance, or a faux pas. But they will never forgive or forget a decision to cover up a mistake. That grievous act—whether in the form of misleading spin or an outright lie—reflects on heart, soul, and character.

I know about slip-ups as well as major mistakes. I've made plenty of both in my business career, and many of them made me want to hide under the desk. But I can honestly say that by taking my lumps and moving on with open eyes—not to mention an open book—each instance became a learning experience with the fringe benefit of delivering an amazing payoff later.

In 1996, I became president of the Philadelphia 76ers. The day after my first season ended (without a playoff appearance), I found myself standing in front of a room filled with Philadelphia's top sports reporters with an apology in hand and a lump in my throat. You see, I had hired a general manager who came with strong NBA recommendations but had no experience as a general manager. My mistake. And my new general manager, in turn, had hired a rookie head coach. Our mistake. So an inexperienced owner allowed an inexperienced general manager to hire an inexperienced coach. The result was predictable, at least with the benefit of hindsight. And my atonement was painful—and public.

I don't think I have ever done anything quite as humiliating as standing in front of the media that day and apologizing to the city of Philadelphia for my mistakes. But because I exercised what I call the "Three R" approach, from that day forward I earned and enjoyed the respect and trust of the press and the public.

So what's the Three R approach? The first step is to assume responsibility for your actions and the actions of your employees by saying the three most important words in the English language in that situation: "I was wrong!"

The next step is to demonstrate regret by apologizing to all those offended with genuine remorse and by sincerely stating, "I'm sorry." Making a mistake is always a challenge to the ego. Offering an apology may seem like a sign of weakness, but the opposite is true. Nothing makes you stronger than letting your ego take a hit in order to do the right thing.

And finally, you must offer a remedy to fix the problem. Every apology requires real repair work. In regard to the Sixers debacle: Starting the day of that torturous news conference, I dismissed the general manager and coach and focused all my energies on finding the best available coaching candidate with the most successful background to help revitalize our city's moribund basketball franchise. Having learned that experience is worth its weight in wins, I successfully recruited Larry Brown, who coached our team to the NBA Championship Finals four years later. My only regret is that we didn't win it all!