It is definitely possible to footnote a table - I tried one myself to see if I could figure out what was going wrong with yours, and it worked fine. I don't know what the problem is with yours other than what you describe about the table being too big to allow footnotes on the same page. Have you tried dropping the point size of the text to make the table a bit smaller that way?

Also, if you've started work in Word but want to continue in Excel, you can also copy and paste your table directly into Excel.