Sefton Central Labour MP Bill Esterson said James Murdoch's apology for The Sun's coverage of the Hillsborough disaster was "too little, too late".
The MP, who took part in the historic Westminster debate on the disaster last month, said the News International chairman's 'full apology' for the newspaper's 1989 reports did little to "heal the wounds".
James Murdoch appeared before the House of Commons Culture, Media and Sport Committee for the second time to answer questions about his company's role in the phone hacking scandal.
Labour MP for Walton, Steve Rotheram, asked the high profile chairman: "Is it not the case that you've failed to show the urgency or the will to deal with unethical practices at News International because, quite frankly, successive chief executives since 1989 have believed that they could do whatever they wanted and get away with it?
"Do you understand the significance of the date I gave - 1989?
"That was when The Sun newspaper published lies about the Hillsborough disaster under the banner headline 'The Truth' and the question I'd like you to answer is - did the fact that The Sun got away with telling outrageous lies in 1989 lead News International into believing they could do whatever they wanted without reproach?"
James Murdoch said: "I'd like to add my full apology to the wrong coverage of that affair. I'd like to add that voice to successive editors of The Sun and chief executives of News International who since that instance have apologised.
"It was 22 years ago and I was far away and a much younger person...but I've since looked at it, I'm aware of the concerns and the hurt that it caused and it's something that we're very sorry for and I am as well."
Bill Esterson said the apology was "long overdue and of little comfort to the families of the 96".
Bill said: "James Murdoch and News International is being pushed into a corner on this issue. It is a disgrace that it has taken this long for the company to recognise its appalling coverage of the disaster.
"The families of those who died, as well as those who were injured and everyone in Merseyside who suffered because of the outrageous lies which were printed by The Sun should never have been put through what they were subjected to by that newspaper. The pain was already very raw for anyone in any way connected to the disaster. It was made all the more painful by The Sun."
Bill said the families he has spoken to in Sefton Central who lost family members on April 15, 1989, say The Sun continues to add to their grief more than 22 years on.
Bill said: "There were 18 people from Sefton who died at Hillsborough that day. I've spoken to a number of their families and the pain they feel today is as fresh as it was 22 years ago.
"I've been lucky enough to spend some time with Barry Devonside from Formby who tragically lost his teenage son Christopher at Hillsborough. He tells the horrific story of how a number of journalists were shouting the outrageous allegations about the fans at him as he was on his way to identify his son's body. It was these lies which The Sun printed a few days later.
"James Murdoch has already conceded that the company will consider closing The Sun down as they did with the News of the World, if the newspaper is found to have be implicated in the phone hacking scandal. But I think he should have closed the paper down long ago for its shameful and hurtful behaviour immediately following Hillsborough.
"The pain it caused to the families and people of Merseyside it caused is indefensible."