A common misattribution.

According to wikiquote that is "a paraphrase of a quote from Aristophanes' Clouds, a comedic play known for its caricature of Socrates."

I'm not sure that actually matters in the current conversation. The quote, even from a satirical play, demonstrates that this was a common enough sentiment in ancient Greece to be worth lampooning. That's nearly as relevant as if Socrates had in fact uttered the quote in earnest.

One of the things that people ought to consider before trotting out that quote is that Athens fell. Socrates' culture is now long dead. The broad stroke of history may be upwards in many ways, but societies can and have fallen apart. Most of the other cultures you may trot similar quotes out from have also effectively fallen, even if they were not destroyed; Victorian England, for instance, does not rule the world anymore. Rome fell after a protracted period in which it was obvious it was becoming weaker. It doesn't take all that much imagination to look about and conclude that we're in the process of "becoming weaker" too.

I don't think this quote proves what people think it does.

I'm not sure it's right to conflate arguments about the possibility of new technology having other-than-positive effects with arguments about the moral decay of society.

I'd argue it's plainly obvious that the end results of technological innovation are unpredictable (how many of us here make novel use of tech to earn our livings every day? who conceived of all this when computers were first imagined?) and that it's plainly obvious that some technological innovation has not been to the greater benefit of man (e.g., the industrialization of war and genocide over the last century)--none of that has much to do with children misbehaving or society losing manners.