You need to use a tense that expresses a past action if “just” is used to mean “recently.” It can be simple past or present perfect (which, a bit confusingly, given the name, is a past tense.) I just did it. Simple past. I have just done it. Present perfect. These two mean the same thing.

Thank you, Phil, for saving me the trouble of pointing that out! As Phil has explained, Ed's answer applies to American English. In British English, the adverb 'just' ( as in "I've just heard the news" or "They've just arrived!") is used with the perfect tense, exactly as you were taught, Sedna. It isn't wrong to say "They just arrived!", but it sounds a little odd to the BrEng ear. We're familiar with the 'just'+simple tense from exposure to American English, but most of us would not use it. NB The same goes for 'yet' and 'already'.

This is actually one of the few differences between British and American English grammar. Ed gave the answer for American English. In British English, however, they usually use the present perfect with “just”, and oddly enough, they consider it to be a type of present tense. (Their reasoning is that the sentence describes the present situation.) You may enjoy my popular mini-article on the subject: https://www.italki.com/discussion/170637