You have admitted your guilt to a crime here. That is the crucial thing. This is enough for the US not to grant you a visa, depending on what you admitted doing.
In US visa law, crimes are classed into two broad categories:
Crimes involving moral turpitude (CIMT) and crimes that are not to considered to involve moral turpitude.
In Visa law, the crimes that ARE considered to involve moral turpitude cause problems when applying for a visa to the US. A person who has admitted to a crime of moral turpitude usually finds their application rejected.
Crimes which do not involve moral turpitude also cause problems if more than one crime which does not have to include moral turpitude was committed.
A CIMT is a crime which constitutes characteristics of evilness and which do not uphold the obligations one owes to society basically. Therefore, crimes such as stealing, arson, violence (excluding common assault) etc all constitute moral turpitude and it is rare for a visa to be granted to a person who has committed one of these crimes unless there has been a large passage of time since the crime was committed.
It is therefore all dependent on what crime you have committed.
You should tell the US embassy about the caution. You are obliged to. Whether they will find out or not after you have submitted a clean Police Certificate is hard to call. I would tell them, because if they were to later find out about it, they may permanently block you from the US as you have deceived them.