A parliamentary committee released a report on Thursday into how the neo-Nazi killers of the so-called National Socialist Underground (NSU) were able to murder 10 people over seven years without being caught.
The NSU is now considered to have been a terrorist group, and its surviving member Beate Zschäpe is on trial in Munich.
She is accused of lending vital support to the group's two gunmen who died in an apparent murder-suicide in 2011.
"We have concluded that we are dealing with massive institutional failures that resulted from a dramatic underestimation of the danger of the violent far-right in Germany," panel chairman Sebastian Edathy said on NDR public radio.
Police and the media had long dubbed the assassination-style shootings, committed with the same Ceska handgun, the "doner (kebab) murders", suspecting that Turkish crime groups were to blame.
German police and domestic intelligence services have since faced withering criticism for bias and failing to think outside the box by associating terrorism only with far-left or Islamist groups, not neo-Nazis.
The almost 1,000-page report calls it "a humiliating defeat for the German security and investigative agencies.”
Despite all the mistakes that were made, the panel ruled out that state security services themselves were involved in the NSU activities, or that they tolerated or supported them in any way.
Edathy said one key lesson was that German police must employ more officers with migrant backgrounds. "I'm pretty sure that, if a leading police investigator had had a Turkish background, investigating authorities would not have taken six years before seriously considering the possibility that racism was the motive," said the Social Democratic legislator.
The report said there had been "major failures and organisational flaws" especially in intelligence-sharing, analysis, the choice of staff and priority setting, while the NSU committed its murders from 2000 to 2007.
Investigators singled out the internal security service, the Federal Office for the Protection of the Constitution, for added criticism stating that it had "undoubtedly failed" and "grossly trivialised" the threat of far-right extremist violence.
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The report also harshly criticised "excesses" in the use of paid undercover informants, including violent leading neo-Nazis who fed the money they received from the state back into their organisations.
Foreign Minister Guido Westerwelle welcomed the release of the report - the product of a 19-month probe with more than 100 witnesses. Speaking during a visit by his Turkish counterpart Ahmet Davutoglu, he said: "It is not only an important step to bring clarity here in Germany, but also an important signal to the world so we can regain trust. It is important for the image of Germany in the world. Terrorism and extremism have no place in Germany."