Murdoch told the inquiry Myler "would not have been my choice" and that he was the choice of Les Hinton, who at the time was News International's executive chairman. He said he thought at the time there were stronger candidates from News International sister title the Sun.
Jay then asked if Myler was a weak individual and wrong man for the job. "I would say that was a slight exaggeration," replied Murdoch. "I would hope Mr. Myler would do what he was commissioned to do."
When asked by Jay whether News Corp had managed the legal risk of phone hacking by covering it up, Murdoch replied: "No. There was no attempt either at my level or several levels below to cover it up. We set up inquiry after inquiry, we employed legal firm after legal firm. Perhaps we relied too much on the conclusions of the police.
"Our response was far too defensive and worse, disrespectful of parliament."
Murdoch later revealed he wished he had closed the News of the World earlier and also admitted he panicked when the phone-hacking affair blew up into a major scandal in July 2011.
"When the Milly Dowler [story] was first given huge publicity, I think newspapers took the chance to make this a huge national scandal. It made people all over the country aware of this, you could feel the blast coming in the window," he told the inquiry.
"I'll say it succinctly: I panicked, but I'm glad I did. And I'm sorry I didn't close it years before and put a Sun on Sunday in. I tell you what held us back: News of the World readers. Only half of them read the Sun. Only a quarter, regular."
Murdoch said he also made a major mistake listening to lawyers when Goodman alleged that others on the News of the World knew about the phone hacking.
"I should have thrown all the lawyers out of the place and seen Mr. Goodman one-on-one and cross-examined him myself and made up my mind, maybe rightly or wrongly, was he telling the truth? And if I had come to the conclusion that he was telling the truth, I'd have gone in and torn the place apart and we wouldn't be here today," he added.
Earlier during the hearing, Murdoch agreed with Jay that the phone-hacking scandal had forced News Corp to drop its controversial £8 billion takeover bid for BSkyB in July 2011.
He told the Leveson inquiry the scandal spiraled into a "great, national" issue after it emerged that the News of the World intercepted the voice-mail messages of the murdered teenager Milly Dowler.
News Corp withdrew its bid for BSkyB in July last year, nine days after the Guardian revealed that Dowler's phone had been hacked by the Sunday tabloid.
Asked by Jay whether the Dowler claims ultimately derailed the bid, Murdoch said: "Well, I don't know whether we can put it down to the Milly Dowler misfortune, but the hacking scandal, yes."
He added: "The hacking scandal was not a great national thing until the Milly Dowler disclosure, half of which - look, I'm not making any excuses for it at all, but half of which has been somewhat disowned by the police."
Murdoch also said he was surprised at the extent of lobbying of the culture secretary, Jeremy Hunt's office by Fred Michel, the News Corp public affairs executive, while the Sky takeover bid was under regulatory scrutiny between June 2010 and July 2011.
Murdoch refused to criticize Michel, but said he may have used "a bit of exaggeration" to tell his son James about his alleged closeness to the culture secretary.
Michel's activities were revealed in a series of emails between him and James Murdoch, the News Corp deputy chief operating officer, that were submitted to the Leveson inquiry and published on Monday.
Hunt's special adviser who dealt with Michel during the Sky bid, Adam Smith, resigned on Wednesday.
Hunt made a statement to the Commons defending his conduct over the takeover bid, but is still facing calls from Labor leader Ed Miliband to resign.
Intellpuke: You can read this article by Guardian reporter Lisa O'Carroll and Media and Technology reporter Josh Halliday in context here: http://www.guardian.co.uk/media/2012/apr/26/murdoch-admits-phone-hacking-coverup