I recently worked a 16 hour shift from 4pm to 8am, and was told that since the new day starts at midnight, I would receive no overtime for the shift. Is this allowed?

That is correct under the law. Each work day stands alone.

I recently worked a 16 hour shift from 4pm to 8am, and was told that since the new day starts at midnight, I would receive no overtime for the shift. Is this allowed?
Did you work again the same day the last 8 hours fell on?

Sockeye has a good point, if you worked on the same day where you worked midnight to 8am then you'd be entitled to overtime.

CA Labor Code defines a workday as:
(a) "Workday" and "day" mean any consecutive 24-hour period
commencing at the same time each calendar day.