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It's clear for me what a native English speaker understand when I say: "I've burnt myself!". But it isn't clear what does it feel or understand if I say: I burnt myself!, maybe: I deliberately tried to kill myself by spilling petrol to my body and let it burn?
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You'd use "I've burnt myself" when it happened recently, i.e. you maybe still wear a bandage or it still hurts.
"I burnt myself" would mean that it happened a certain time ago already, so maybe only a scar can still be seen or/and it doesn't hurt anymore.
Comments  
to say "I've burnt myself!" has only the meaning that you have physically burned yourself. It doesn't give any indication as to why or how you've done so. It's simply a statement.
 Pemmican's reply was promoted to an answer.