Your vexation is understandable. While it sounds like something Churchill might have said, no competent, authoritative quotations source unequivocally attributes this quote to him. The last word of the quote is variously phrased as "winners," "conquerors," and "victors." That alone indicates that its origin cannot be firmly established.
The best that can be said of it is that it is idiomatic or axiomatic, that is, it has been accepted in the popular consciousness as a "truism." Contemporary U.S. historian Howard Zinn acknowledges this fact and uses the idea to write the history of the U.S. from the standpoint of those who were oppressed by and/or the victims of the exploits of the "victors."
If you are looking to use it in a paper, you could footnote is as "attributed to Winston Churchill, but of unknown origin."