The answer is in the OED's definition of buriels1, namely

  1. A burying-place; a sepulchre, tomb.

  2. An interment, funeral.

Note that both meanings are already singular: A burying-place, An interment, etc.

So the "correct" formation of burial would be buriels. It was "falsely" constructed because the singular, Old English word was mistakenly believed to be a plural, French word. From the OED's etymology of burial (just after the part you cited):

in later times associated with nouns in -al from French, such as espousal-s.


1"ˈburiels, n." OED Online, Oxford University Press, June 2017, www.oed.com/view/Entry/24975. The etymology of buriels is helpful in pointing out how a singular English word ended up ending in -s (among other things). Note that the OED Online is unfortunately a prescription service (behind a paywall). However, many folks, especially in the UK, will have access through their local public library, and most students should be able to access through their institution's library. More info here: http://public.oed.com/about/free-oed/

2"burial, n." OED Online, Oxford University Press, June 2017, www.oed.com/view/Entry/24969.