I didn't do any exit passport control when leaving Japan. What should I do?

Managing to leave Japan without an exit stamp or having your passport inspected at all is extremely irregular, and I'm quite astonished that you managed to do so, especially by accident. You are almost certainly registered as still being in Japan and, if you do nothing to fix this, likely to run into a lot of trouble the next time you visit.

Your best bet would likely to be to contact the Immigration bureau at the airport you left from, in your case Kansai (tel. +81-724-55-1453) and ask for their guidance on how to sort this out. Office contact details are available here: http://www.immi-moj.go.jp/english/info/

Per the site above individual information will not be disclosed by email, so you'll need to call, and I'd start by just stating that you noticed there's no exit stamp on your passport and.you wanted to confirm that your exit was correctly recorded. However, in your shoes I would definitely insist on a written statement that this has been all sorted out. I would also expect that they will -- with some justification -- blame you at least in part and more probably than not ask you to write a "gomen nasai" apology letter for (unwittingly) violating the law, but I would not expect other lasting consequences if your record is clean and your story otherwise checks out.

Update: The OP has clarified that they used the new automated exit gates, which indeed do not stamp your passport (and my bad for not remembering this, since I used one last month when I flew out of HND!). However, using the gates most definitely does require scanning your passport, it's just done by a machine and not a human.

As jpatokal says, you should contact the appropriate authorities in Japan. However, something else you should do is to collect evidence of your departure. If the Japanese authorities accuse you of overstaying, you should have evidence that you didn’t.

You should keep your boarding passes and any receipts from airport purchases etc. Perhaps your passport was stamped on arrival in another country after you left Japan.

If there is a Japanese embassy or consulate near you, you could go there in person in order to demonstrate unequivocally that you are no longer in Japan. Ask them to give you some written document saying that you were not in Japan on that date.