I practice law in Arizona. Here, I would certainly loom into whether your statements were voluntarily given. But just being intoxicated or tired or hungry, alone, probably wouldn't be enough. In fact, when the cops interrogate, they try to "soften you up" by letting you get hungry, tired, desperate, etc. If you are drunk, the interrogator knows your judgment is impaired and that is the time to strike. And as they say: "loose lips sink ships"
This is not legal advice, it is only for public informational purposes.
Certainly your intoxication raises a number of issues regarding the reliability of your statement: 1. Did you knowingly, voluntarily, and intelligently waive your right to remain silent when you gave the statement? 2. In light of your intoxication, was your recollection accurate or trustworthy? You want to contact an experienced criminal defense attorney to more thoroughly review the facts and circumstances of your statement, with a focus on your intoxication.
Do not speak with the police any further, and if you are going to attempt to give an amended statement, then that is something you should only do on the advice of counsel after having had a chance to meet and discuss all your options. While you wouldn't necessarily get into any more trouble for simply wanting to retract your statement, you could complicate matters and harm your defense if not done properly with counsel.
Fell free to contact me to discuss it further.
It is alweaays better to not talk to anyone. Your Lawyer, depending on the circumstances, wll have to appraise whether you want to change what you said in light of many different factors. Please follow his/her judgment and don't tery to repair irt yourself.