When teaching students about the hydrogen atom we have a tendency to assume the proton is fixed and then just ignore it. Then we just have a single particle, the electron, moving in a $1/r$ potential. This approach is so common it even has a name - it's called the Born-Oppenheimer approximation. Viewed this way it makes sense to talk about exciting the electron because, well, the system we are considering only has an electron.
However the Born-Oppenheimer approximation is indeed only an approximation. Even though in an atoms the nucleus is far heavier than the electrons it too will move due to the interaction with the electrons surrounding it. So in reality you can't separate the energy levels of the electrons from the nucleus. You have a composite system of electrons and nucleus and you can only talk about the energy levels of the whole atom.
So when you add a quantum of energy to an atom you are not just changing the energy of the electrons, you are changing the energy of the nucleus as well. That's why is it more correct to talk about a transition between energy states of the whole atom.
having said this, it's usually an excellent approximation to treat the nucleus as fixed and just talk about electron transitions. I would guess most of us have used this sort of phrasing.
If you're interested in learning more about the energy levels of atoms see my answer to Why do non-hydrogen atomic orbitals have the same degeneracy structure as hydrogen orbitals?.