Well, I'd say it's more than the Internet -- most classic SF writers missed computers period, even if they have intelligent robots in their universe, which is odd. People were described as plotting the course of spaceships using pen and paper and slide rules, while their trusty robot pals were apparently no better at math than the humans.
Maybe not quite "old SF", but the undeservedly nearly forgotten John Brunner described a computer network akin to the Internet in his 1975 The Shockwave Rider.
And then there's E.M. Forster's (yes, the Howard's End and A Passage to India guy) The Machine Stops from 1909(!). In this over 100-year old story, you have basically the prediction of the Internet, e-mail, and even Amazon.com. And the moral that all of this might not be 100% great as people are shown as not interacting in person anymore (also kind of true).