That's what the 'exception of a few nutrients' essentially covered. The Irish depended upon the potato so greatly that the potato famine caused mass starvation when it struck.
Obviously you shouldn't depend on any one food, as a restricted diversity in your diet is very unhealthy. The Irish supplemented it with goat's milk to provide the last piece of their diet that the potato didn't provide. Aside from that, it yielded most of the calories, vitamins, and minerals that they needed.