You are in a present-framed situation, hence the use of present perfect. 'just' is somehow ellipsed:Originally Posted by sardine
"I have (just) finished my HW, so let's go out to play"
(the action has a result in the present: now you no longer have HW to do, so you can go out)
Now, if you're refering to a situation that happened at a particular time in the past, then you can use the past simple:
"[yesterday] after I finished my HW, I went out to play"
My humble explanations...