I don't think so. It is not about successfully completed 'not phoning'.
The perfective here is used in its usual meaning 'single action', 'action as a whole', action that has no significant time duration. We are just saying that this single action was not performed.
In my opinion, the choise of aspect is rather arbitrary in this particular example.
'Я не позвонила' - I didn’t perform the action of phoning.
'Я не звонила' - I didn’t phone. (I had a chance to phone but I never phoned.)
Aspect here does not tell us any essential information, and the grammar does not force the specific one to be used either, so both can be used:
- Ты звонила заказчику?
- Я не звонила. / Я звонила.
- Ты позвонила заказчику?
- Я не позвонила. / Я позвонила.
It should be дозвониться:
Я не дозвонилась.
Я не смогла дозвониться.
Мне не удалось дозвониться.