I wouldn't expect that to change after a nuclear war, especially in a world without contraceptives.
That aside, there really needs to be more understanding of the difference between species extinction and cultural extinction.
Humans could survive for hundreds of millennia in a devolved state. They wouldn't be particularly human by our standards, but they'd have the same DNA.
But our culture would be gone. All the accumulated knowledge would be wiped out, and it's very possible nothing like it would ever return.
DNA is fairly robust. Culture, knowledge, and rationality are extremely fragile. We're not doing an outstandingly job of preserving them even without a nuclear war, and I can't imagine a nuclear war would make the situation any better.
We may lose the know-how / capacity to produce certain things, such as we did with Damascus steel or roman concrete, but we are an endlessly resourceful species. I place my faith in our ability to adapt and come up with new solutions as required.
Whatever technological knowledge survives in the books, most of it will be useless for centuries, as we regress into pre-industrial level of technology and can't climb back out - we've already mined out all easily-accessible high-density energy sources that are necessary for reindustrialization.
Simple computers are relatively easy to make with today tech. Software exists already.
Nor is there a particular shortage of hydrocarbons to burn, with consumption reduced so much due to population loss and reduction in quality of life. Consider that US today emits more than 200x carbon into the atmosphere than it did in 1850, and that this growth has been exponential. So what we consider one year worth of reserves today, could provide energy for many decades in this hypothetical.