First of all, I think that that kind of serious constraint is mostly a stunt. It can be interesting, once. Usually an introduction or blurb for that sort of work explains the constraint, and why the author adopted it. Sometiems, particularly with a milder constrant, the reader is just left to figure it out.
For example, "Uncleftish Beholding" (1989) by Poul Anderson begins:
For most of its being, mankind did not know what things are made of, but could only guess. With the growth of worldken, we began to learn, and today we have a beholding of stuff and work that watching bears out, both in the workstead and in daily life.
The underlying kinds of stuff are the firststuffs, which link
together in sundry ways to give rise to the rest. Formerly we
knew of ninety-two firststuffs, from waterstuff, the lightest and
barest, to ymirstuff, the heaviest. Now we have made more, such
as aegirstuff and helstuff.
This is in effect a popular science article written in an alternate English pruned of words with Latin and Greek roots, relying on words (and new compounds) with germanic roots instead. This is a significant constraint, but the first publication did not, if I am correct, explain it. Later re-printings did, in an author's note or introduction. See this Wikipedia article for more information.
For another example, i once wrote a couple of short pieces where we were presented with one character's thoughts, but not his words, and heard another character's words, but not his thoughts. Sort of a variant on the classic one-sided overheard telephone conversation. It worked, but was a bit clumsy at times, and would not have worked for more than a few pages.
So if you choose to engage in such constrained writing (and why not) I would suggest including an introduction in which you state the constraint. But there is no rule on the matter.