Earlier quoted context omitted.
Tee hee you used it! Really though, I think there is a big difference between "Very tired" and "exhausted". Although the technical mind I think is bugged more about precision rather than flow or poeticness of speech Ι think we can appreciate it...
Especially in certain situations like "I'm not very tired". Offhand you could say "I'm not overly tired" or "I'm not too tired", but those could subtly change the meaning of what you're trying to say or sound unnatural in everyday speech.
Tired, exhausted, washed up, worn out, fatigued, beat, weary, run down, depleted...