No, there is no such requirement. The traffic ticket was validly issued. You admitted directly to the cop that you did something wrong. There's usually many different ways to fight traffic infractions, but your options are severely limited since you admitted the violation.
Since you approached the officer and admitted guilt, the situation is more complex than normal. If you disagree with the ticket (and if it is just a traffic ticket, not a criminal citation for reckless driving or some such) then you probably want to contest the ticket. In that case, keep in mind that you only have a limited time to request to contest. There are some good traffic ticket attorneys in your area who could (once retained) review the police report, and see if there is enough in it to support the infraction. Call around, and I'm sure you'll find one you would want to work with.