Speaking at Advertising Week Europe in London on Wednesday, Morgan said: "None of my kids read them – it’s all online and on phones.
"Too many journalists think it's terrible – get over it! It's the new world – we’re not on penny farthings any more."
Morgan edited the News of the World in the 1990s before becoming Daily Mirror editor, and his current roles include editor-at-large for the Daily Mail US. "The Daily Mail is the biggest English speaking newspaper in the world because it made a decision very early on not to make people pay, and it was right," Morgan said. "That's why it is so successful – the business model that works is massive traffic and lots of advertising."
Interviewed on stage by Mediacom MD Claudine Collins, Morgan said the Leveson Inquiry into press ethics and its aftermath has left Britain with a "muted" press. He made the comments in relation to reports that newspapers had purposely avoided writing stories about the private life of Culture Secretary John Whittingdale over fears of repercussions.
"The tale that’s being told about all national newspapers ringing each other up and agreeing that they weren't going to do the story [about Wittingdale] is not true – that didn't happen," said Morgan. "These guys are competitors. Post-Leveson Inquiry, there was not a chance that the story was ever going to be published.
"The Leveson Inquiry was very good – but I think it has left us with a muted industry. This country, good or bad, has one of the most free presses in the world. But the day you mute it is the day we get our own Vladimir Putin."
Morgan, who in recent years has carved out a media career in the US as host of shows such as Piers Morgan Live on CNN until 2014, also waded into the debate over the American election nominees, saying Donald Trump has a "very good chance" of being the Republican presidential candidate.
"If you're a Washington or Californian elite, of course you see him as the devil incarnate. But the rest of the US think he's brilliant as he's not a politician and he's there for the little man.
"Hillary Clinton is not as popular as people think, and [Trump] is more popular than people think. In Texas and Florida, people are genuinely terrified by terrorism so he's playing to a real fear."