More information is needed. If you are a naturalized Citizen, then I have to assume that you have a U.S. Passport.
If you were naturalized 'and' given a certificate in addition to getting your I-551 green card, but were a U.S. Citizen at the time that you committed the offense 'and' pled guilty, then you should not lose your citizenship. However, you should check with your criminal attorney, who handled the case before you leave the U.S., since there may be restraints on travel.
You may have to file U.S. Tax returns, but this is a separate matter. Finally, you should decide whether you plan to assert dual citizenship. There can be conceivable challenges that may exist as a result. However, this are issues separate from whether you can travel and relate to how you will travel.
If you are still confused, then I strongly recommend an appointment or teleconference with an experienced immigration attorney, who can take the time to explain the situation to you.
The above is general information and does not create an attorney client relationship.
Generally, staying in the country isn't a requirement in a summary probation. However, it is entirely possible that it is in your case.
You may have received some documents when you had a disposition of the case in question. You should read the fine prints. You can also contact the probation office of the court in which your case was held and ask whether such a condition was imposed in your case.