On the one hand, you lose "to" your rival. On the other hand, a defeat is done or comes "from" them (there are some search results for the latter but mainly from second-rate publications). I think you can do both but 'to' is better. Am I right?
I am talking about sentences in this form:
"[subject] suffered a defeat to/from [object]"
Liverpool suffered a defeat to Tottingham.
The Labor Party suffered a defeat from the Conservative Party.