Michael Bloomberg almost certainly wouldn’t have become the mayor of New York City — or a billionaire — if the powers that be at Salomon Brothers hadn’t done him a huge favor in 1981.

They fired him.

Bloomberg and 61 other partners at Salomon walked into work one day and got the news that they were being dumped. The investment firm was merging into Phibro Corp. and, ahem, their services were no longer necessary.

Bloomberg’s firing did come with a check for $10 million from proceeds of the sale, and the dismissal gave him the incentive to establish the Bloomberg financial information empire, which now generates more than $3 billion a year in revenues.

His tale and others from the famous and the not-so-famous are part of Harvey Mackay’s new book, “We Got Fired! … And It’s the Best Thing That Ever Happened to Us” (Ballantine).

Although obviously most people don’t find their pink slips accompanied by anything close to a $10 million check, Mackay said in an interview that Bloomberg and many other successful people overcame their setbacks by having a “I’ll show those guys they made a mistake” attitude.

He explained that many workers who get dumped take the essence of that approach and turn it into something negative by trying to sue or badmouth the employer, rather than using it as inspiration to create a better life for themselves.

“You can’t play the blame game,” Mackay said. “You can’t saw sawdust. It’s done. Let’s move on.”

The author said that the biggest cause of failure for companies and workers is arrogance, which causes people who have been fired to assume that there is something wrong with the boss or the company, in many cases blaming vengeance or office politics.

“They will not look in the mirror or go to friends and get the real reason they were fired,” Mackay said. “A lot of people are in the wrong job.”

One such person Mackay interviewed in the book is actor Robert Redford, who got fired from several jobs. Redford knew exactly whom to blame: himself.

“I would become distracted and my concentration would wane,” Mackay quotes Redford as saying. “I couldn’t apply anything I felt strongly about to the jobs I had. It was only a means to keep me going until I could figure out what my path was.

“That occurred to me when I went to Europe and studied art. During that year and a half I realized that I had to do something dealing with art. Art led to acting and everything else.”

Mackay explains that people who get fired not only need to understand why it took place, but have to be able to tell potential employers what they have learned from it.

“The resume that explains an unhappy firing situation clearly and honestly is not the one that potential employers find suspicious,” Mackay writes. “The suspicious resumes are the ones with unexplained voids or breaks in a career.”

My two cents: In too many instances, people’s explanations of why they were fired points fingers at bosses or colleagues, which is a mistake — no matter how many people would agree with you. Potential employers want you, not your baggage, and too many fired employees come across as bitter or cynical.

What you can and should do in that circumstance, though, is have a reference from your old company if you were there for very long. A supervisor is best, but at least you should have a co-worker or client who can say nice things about you.

And if that person happens to spell out how badly you were treated or how incompetently management behaved, it comes across a lot better than if you were to say it.

Under the old “every cloud has a silver lining” theory, sometimes people who get fired or quit a job without having anything lined up are better off than their cautious counterparts. They will begin job hunting with a passion and look for less obvious avenues to pursue, which is much harder if you’re working 40 or 50 hours a week.