The criticism comes after a vigorous stand by Miliband against the right-leaning paper following its claim on Saturday that his Marxist intellectual father "hated Britain" and despite an apology from The Mail on Sunday for sending a reporter to a Miliband family memorial.
It is understood that the situation has been deemed so serious in Labour's ranks that both Bob Roberts, Labour’s director of comms, and Tom Baldwin, Miliband’s adviser on strategy and comms, are working on the issue.
Dominic Ponsford, editor of journalism trade title Press Gazette, said that the Mail's editor Paul Dacre had shown "courage and indefatigability" but added the newspaper's coverage was likely to be an "own goal" in the context of the negotiations over a new system of press regulation in the wake of the Leveson Inquiry.
The newspaper industry's proposals for regulation, which it has put forward as an alternative to the tougher cross-party proposals supported by pressure group Hacked Off, are to be studied by the Privy Council next Wednesday (9 October).
The council, which is made up of politicians, will decide whether to seal a Royal Charter approving the industry's proposals.
"The Miliband coverage is not helpful in the context of the current debate over press regulation as we come to the crucial juncture next week," Ponsford said. "It does make it more likely that politicians are going to side with Parliament’s Royal Charter, the cross-party deal with Hacked Off."
The proprietor of the newspapers Lord Rothermere has since sent a letter of apology to Miliband for the memorial incident, and two Mail on Sunday journalists have been suspended amid an investigation.
However the Mail has not backed down from its initial attack and nor has Miliband dropped his criticism of the paper. This morning the Labour leader called on Rothermere to take a "long, hard look" at the "culture and practices" of his Mail titles.
Miliband told BBC Radio 5Live that Rothermere’s response was an "an important step" but added that he wanted to know "how these practices happen".
Managing partner at College Hill Tim Fallon, who earlier in his career worked in the Labour Party press office, said that the Mail’s opinion piece and the reporter's appearance at the memorial "crossed a line".
Fallon said: "The media environment has always been quite brutal but what the Mail did was go beyond a certain line and it has come out badly from this."
"It has demonstrated not just a distinct lack of judgement but a lack of values. It has not handled this situation well, but I’d be surprised if it did anything more."
Fallon said even though "strategic" reasons did not account for why Miliband spoke out, the Labour leader "has demonstrated that he has character and a set of values".
"He is shown to be family-focused, and like a normal person who will not be pushed around. It is an issue with which a voter can connect."
Ponsford added: "I think the other newspapers sense that this is a story where most people’s sympathies appear to be with Ed Miliband. Most people can relate to the idea of their deceased father being attacked in a newspaper and wanting to defend them."
The executive director of the Telegraph Media Group, Baron Black of Brentwood, who is closely involved with the newspaper industry’s regulatory negotiations, declined to comment on whether he thought the Mail’s coverage was an own goal for the press.
The Daily Mail had not responded to a request for comment by the time of publication.