In a way he did even more directy. Every time he talked about the khandas, he was talking about anatta; those two are teaching the same thing. And he said, the khandas are impermanent and therefore suffering. He directly explains the link between those and what exactly is suffering. One only needs to make the step that there is nothing outside of the khandas and it all fits together beautifully. And to make sure we can't intellectually find a way out, the Buddha said "whatever form/../consciousness, near, far, subtle, gross etc is the aggregate of form/../consciousness".
Sure, some people still try to define some atman outside of the aggregates, either in a free will or in a sort of consciousness. But with my humble understanding, the Buddha included all their ideas by this statement as to be actually anatta & dukkha. And if we can let it all go, there'd be nothing to loose. This is how I understand the Buddha's teachings.