Technically, you can't appeal on this basis since the record (trial transcript, clerk's minutes, etc.) will not show what your attorney did or did not tell you, what you would have done in response, etc.
However, you can seek reversal of your conviction through a petition for a writ of habeas corpus. You would face a very difficult time doing this, but it is possible. You would have to show:
1) Your attorney gave incompetent advice,
2) Had he given correct advice, you would have agreed to plead guilty, and
3) Had your attorney approached the DA, he or she would have offered you something better than what you received.
Note that the law is VERY tough toward defendants in this situation. The California Supreme Court has repeatedly made clear that they don't want to allow convicted defendants with "buyer's remorse" about their decision to plead guilty (or not plead guilty) to easily avoid the consequences of their decision.
Good luck to you –