Нам надо спешить или мы опоздаем на концерт. Нo usually means but, not ever or.

спешить is imperfective.
опоздаем is in the Future Tense so it automatically means that it's perfective.

There is no rule that you need to use imperfective after надо, in fact you could use the perfective form of to hurry which is поспешить:
Нам надо поспешить, а не то мы опоздаем. And this would mean quite the same thing, in fact this is the same thing.

Other example:
I need to leave:
Мне нужно идти - Мне нужно уйти.


But make no mistake, using imperfective or perfective after надо is not always interchangable.