It seems to be consensus on this site that being denied a US visa makes it practically impossible to get an ESTA. I agree on the 'practically' part but I can't seem to find anything definitive from official sources.
The question is not about the likelihood of being granted an ESTA after a visa refusal. It is about whether a visa refusal makes one officially ineligible.
The Ineligibility section on this VWP page ustraveldocs.com (which I understand is official, despite the dodgy name) makes no mention of visa refusals.
The State Department VWP page states only that
A recent visa refusal for any reason could result in denial of ESTA authorization, additional review at the port of entry, or denial of admission to the United States. If you are uncertain if you qualify for VWP travel, you may apply for a visa.
but does not categorically state that a visa refusal results in VWP ineligibility.
This CBP help article is more strongly worded in that it says an ESTA denial is the 'most likely' result given a visa refusal but still comes short of saying anything about ineligibility.
If you were previously denied a visa, or previously refused entry to the United States, or previously removed from the U.S., your ESTA application will most likely be denied.
There are claims on the Internet about having been approved for and using an ESTA successfully after a visa refusal but I won't bother to include those for obvious reasons.
Again, the question is not about the likelihood of being granted an ESTA after a visa refusal. It is about whether a visa refusal makes one officially ineligible.