You're thinking of Asimov's essay "The Ancient and the Ultimate". It was originally published in the January 1973 edition of the Magazine of Fantasy & Science Fiction. It was later republished in The Tragedy of the Moon (or here), one of Asimov's essay collections, and later in Asimov on Science.
The essay is referenced in the Isaac Asimov FAQ on Asimov Online:
What is the title of the essay that Asimov wrote concerning the
ultimate self-contained, portable, high-tech reading device of the
future which turns out to be a book? Where can I find it?
The title of the essay is "The Ancient and the Ultimate". It was first
published in The Magazine of Fantasy and Science Fiction in January
1973, and appeared in the Doubleday collections The Tragedy of the
Moon (1973) and Asimov on Science (1989).
The essay is written as a response to the idea that video cassettes might replace books. The essay explores the idea of cassettes and players being improved to the point of perfection (smaller batteries, better displays, etc) and concludes that the perfect cassette player is a book.
This page has some quotes from the essay:
You’ll have to admit that such a cassette would be a perfect
futuristic dream: self-contained, mobile, non-energy-consuming,
perfectly private, and largely under the control of the will.
Ah, but dreams are cheap so let’s get practical. Can such a cassette
possibly exist? To this, my answer is Yes, of course. The next
question is: How many years will we have to wait for such a
deliriously perfect cassette?
I have an answer for that, too, and a quite definite one. We will have
it in minus five thousand years–because what I have been describing…
is a book!
Some other pages talking about the essay: