Mr Miliband said Sir Desmond De Silva's report made "disturbing and uncomfortable" reading, as he urged Prime Minister David Cameron to go further and order a judicial inquiry into the murder of Mr Finucane in 1989 by Loyalist paramilitaries.
Sir Desmond's report found British security forces colluded in the murder and then obstructed the investigation into finding those responsible.
Speaking in the Commons, Mr Miliband said Labour began to set up a public inquiry, recommended as a result of the Weston Park agreement between the British and Irish governments in 2001, before it lost the last general election in 2010. He said failing to hold a public inquiry was "at odds" with the peace process, adding that the De Silva investigation had its limits.
Mr Miliband said: "We must, as the United Kingdom, accept that our state sometimes did not meet the high standards we set ourselves through the Northern Ireland conflict. Anyone reading this report will believe it is an appalling episode in our history. All sides of the House believe that we must establish the full and tested truth about Pat Finucane's murder but on this side of the House we continue to believe that a public inquiry is necessary for his family and Northern Ireland."
But Mr Cameron said he did not think a public inquiry would necessarily uncover more details. De Silva had access to all the documents, the Prime Minister said, adding that decisions to redact any information was a matter for him.
Mr Cameron said: "If we look at the other inquiries that were started after the Weston Park agreement... some of those inquiries took five, six, longer years, cost tens of millions of pounds and I don't believe actually got closer to the truth than De Silva has done in his excellent and very full report. To me, the real question, what is the fastest way to get to the truth? What is the best way to lay out what happened and to provide the security that does? I think the process we have been through is right."
Mr Cameron added: "In the end I think what matters is getting to the truth, and I can't think of many other countries anywhere in the world that would set out with this much detail, with this much clarity, what went wrong. It pains me to read this report. I am so proud of our country, of our institutions, of our security services, that keeps us safe. And it is agony to read this report but it is right that we publish it. You don't need a public inquiry with cross-examinations to do that. You just need a Government that is bold enough to say 'Let's unveil what happened, let's publish it and then let's see the consequences'."
SDLP leader Alisdair McDonnell said he stood with the Finucane family at the solicitor's funeral, adding that he would also like to see a public inquiry to get to the truth. He said: "I want to say clearly that I was very proud to stand with the Finucane family in those desperate times at Pat's funeral as they buried Pat. The SDLP and I will stand with them today and indeed into the future because we support their demand for a full public inquiry. We feel that we have still only got half the truth out here. There are people out there who should be held to account even though it is 23 years too late."
Labour former Northern Ireland secretary Shaun Woodward said the report had uncovered 287 instances of information, often highly classified, being passed by the British security forces to loyalist groups. Turning to the Prime Minister, he added: "I am afraid that this report is just the beginning of a set of questions and it is not a set of answers. Your statement was indeed grave and I say to you that I really think that for the reputation, and good reputation, of the security forces, it would be wise to reconsider (having a public inquiry). They have been very badly damaged by the conclusions of this report and for the good of their reputation and for the Finucane family, will you reconsider having a public inquiry?" Mr Cameron replied: "I don't think that a long, open-ended, very expensive inquiry would actually get further than what we have in this report, which has been an exercise in opening up the Government, the security services and the police to the maximum extent possible. And of course if there is a public inquiry that puts a stay on any potential prosecution."