Does 'дозвониться' mean 'to phone (someone)' in a general sense, or does it mean 'to get through (to someone) on the phone.'?
If it's the second one, then 'Я не дозвонилась' translated into English would be 'I tried to phone but couldn't get through'. I was actually talking about a situation where someone had just not picked up the phone and tried to call.

The information I had about use of perfective/imperfective with negated verbs goes like this:-

'Aspects in the negative
Using the negative with perfective verbs indicates the person failed to do that action. Using the imperfective will normally simply mean that it didn’t happen
Я не позвонила - I failed to phone (perfective) (but I was expected to)
Я не звонила - I didn’t phone. (imperfective)'

Which seems a bit obscure to me.

I can see RedFox's way of thinking. If you say 'Я не позвонила' it implies that you are discussing one single action of phoning, which in turn could imply that you were expected to phone.
Whereas 'Я не звонила' would just mean 'I didn't do any phoning'

As far as I understand it, aspect in general seems to go like this:-

Imperfective:-
Used when an action doesn't have one beginning, a middle AND an end. This can either be because it didn't happen, happened but was reversed, was attempted for a while but not completed successfully, happens repeatedly/habitually, is still happening (ie present tense,) or simply when you want to emphasise the fact that it WAS or WILL BE ongoing (past tense, future tense.)
A bit like just the pure action of something, the process of something 'ongoing', so to speak.

Perfective:-
When an action has one beginning, a middle AND an end (and isn't 'undone' in some way afterwards.) But this can include actions succesfully completed repeatedly, if you state that they happened a particular number of times.
So it's like a concrete example of some action being performed, and no longer being performed because this itteration of it has ended. Which is why it can't be used in present tense.