When you have realized that you have done a mistake in the report you have submitted to the management. How do you manage the situation?

If the mistake is unimportant, just forget about it. 

If it is big, not reporting it would be gross misconduct.  The company might make a bad decision.  People - other than you - might lose their jobs.  If it's big enough, the company might even go bust. 

Big mistakes always get noticed in the end, unless you are deceitful, clever and lucky enough to invent a convincing stream of lies.  History is littered with examples of companies that went bust because somebody covered up a mistake.   The person responsible usually ends up in jail.

Basically, you have two choices

a) hope to get away with it now, on the understanding that the consequences in the future will be much worse

b) fix it now, with a real chance of keeping your job or, at the worst, being allowed to resign and get another job.

I was knew somebody at another company who made a mistake.  She noticed within half an hour and tried to fix it (before telling her boss) but the markets have moved the wrong way and it cost the company about the same as her salary.  She undid the mistake and confessed.  I had quite a long conversation with her boss about it, and the consequence was that she kept her job.  Partly because she was normally an excellent employee, and partly because she had handled the situation correctly.   We're all human, and it was an honest mistake.  Both her boss and I knew that it could easily have been either of us.  Had she not handled it correctly, it would have been discovered eventually and she would have not worked in the industry again.

In other words, not reporting the mistake is a MUCH bigger sin than making it in the first place. 

Well, I take the responsibility for the err. Whether made by me personally or my staff, I always own my mistakes. With some management it will buy me respect with some it will cost me my job. Simple as that.