You can insert ordinary linked footnotes in table cells, and they will appear at the bottom of the page ("Below text" just means that they appear immediately below the last line of text on short pages as opposed to at the bottom of the page). One caveat
is that this works best for short tables or at least tables with fairly short rows. I have seen documents in which users used a table for large amounts of text (for the purpose of having two side-by-side translations of a text, for example) and did not start
new rows at regular intervals. The problem is that Word "holds" the footnotes for the page on which the row ends. If you keep piling up many pages and multiple footnotes in a single row, eventually you get to the point where there is not room for all the footnotes
on the page where the row ends, and so Word just discards them: they can be seen in the Footnotes pane in Normal/Draft view, but they will not appear on any page in the printed text.
Also, as stated, the proper place for footnotes is at the bottom of the table, and the only way that footnotes at the bottom of the page will work for this is if the end of the table is the end of a page. And of course if the table extends over multiple
pages, then some of the footnotes may appear on pages other than the last (which may actually be preferable). General notes, such as "Source" notes or legends should absolutely be at the bottom of the table.
So yes, putting them in a bottom row is still the best method, and they do have to be manually inserted. Ordinarily, however (and especially if there are other "ordinary" footnotes in the document), superscript numbers are not used in tables. If the tables
consist primarily of numbers, then superscript letters are preferred. Otherwise, a sequence of *,
†, ‡, etc., can be used.