Do you have to use the 上一次的 construction? Could you just say 上次足球比赛？
Does there not need to be a proposition in the Chinese sentence to clarify that the action happened "in" or "at" the competition?
Not necessary. 上一次的足求比赛 is used as a topic: "As for the last football competition, they were first."
Fair enough. It's easy enough to understand when the comma is included, but tough for me to parse, otherwise.