"I just sent it" and "I have just sent it" have the same meaning. In general the simple past 'sent' focuses on the action itself and the present perfect 'have sent' focuses on the result of the action, but in some cases, perhaps in many cases, there is very little difference. If you indicate a specific time reference like 'a few minutes ago' you must use the simple past. Say "If I want to say that I sent something a few minutes ago . . ."
There's a problem with your question. Your original post - and the title of your thread - implies that you're asking about the difference between present tense "I just send" and present perfect "I have just sent".
But your second post seems to indicate that you're asking about the difference between past tense "I just sent" and present perfect "I have just sent".