Hm. This is tricky. I wouldn't use the word cause there. To say that the coach caused his team to win suggests that he got them to do something that they might not have wanted to do. That doesn't make much sense here, since they probably wanted to win anyhow. You could say that he inspired them to do their best or that he got their best effort out of them or that they played their hearts out for him. All of those would make sense.

:)