The rail infrastructure company had pleaded guilty at St Albans Crown Court in Hertfordshire to breaching health and safety regulations which led to a high-speed train derailing at a faulty set of points.
NR's predecessor Railtrack was the infrastructure company in charge at the time of the crash but NR has shouldered the responsibility.
Sentencing NR today, Judge Andrew Bright said the crash of the London to King's Lynn train just outside Potters Bar station just before 1pm on May 10, 2002 was a "catastrophic accident".
He said the lives of the bereaved families had been devastated and that Railtrack's procedures and standards were "seriously inadequate".
Judge Bright and some of the bereaved families highlighted the fact that, as NR is a not-for-dividend company with no shareholders, any fine for NR would have to be paid from what the judge said was "an income which is substantially derived from public funds".
Perdita Kark, the daughter of Austen Kark, one of the passengers who died in the crash: said: "It's offensive that I pay a fine for something that killed my father."
Train drivers' union Aslef said it was "ludicrous that managers responsible for rail safety walked away unscathed while the public picks up a £3 million bill".
NR said it accepted the fine "as we accept the liabilities inherited from Railtrack".
The company added: "We say again today that we are truly sorry."
The Office of Rail Regulation (ORR), which brought the case against NR under the Health and Safety at Work Act, said that safety on the railways had improved but could be strengthened further.
Pat Smith, 63, whose mother Agnes Quinlivan, 80, was killed by falling debris as she walked close to Potters Bar station, said: "I just hope that other families in the future are not treated as shabbily as we were by the rail companies, and I include Network Rail in that."
Maintenance company Jarvis - which was responsible for the section of track at Potters Bar, but is now in administration - also faced charges but the ORR decided in March not to proceed as the prosecution was "no longer in the public interest".
Six passengers on the West Anglia Great Northern express - Mr Kark, Emma Knights, Jonael Schickler, Alexander Ogunwusi, Chia Hsin Lin and Chia Chin Wu - were killed.
They were in the train's fourth carriage which became airborne after derailing and ended up getting wedged under the canopy of the station.
NR admitted failings over the installation, maintenance and inspection of adjustable stretcher bars which keep a moveable section of a track at the correct width for train wheels.
Judge Bright said Railtrack had had no specific guidelines for installing, maintaining and inspecting the kind of points that failed at Potters Bar.
Serious faults with the points "could and should have been identified sooner", he added.
The company's failures put the travelling public and train crews at the risk of serious injury, the judge said.
Assessing how far up the Railtrack organisation the failings went, Judge Bright said that although there were very serious failings by Jarvis, "overall responsibility for the breach of duty lay with Railtrack at senior management level and their failures were significant and extensive".
The judge said there were individuals who bore responsibility for the maintenance failures.
He added: "I do not doubt that those who lost loved ones in the crash might have hoped to see those individuals held to account for their failure.
"However, they are not before the court and it's Network Rail Infrastructure who fall to be sentenced for an offence committed by Railtrack plc."
Judge Bright said that, although NR was making progress on all 10 points of concern raised by the judge presiding over last year's inquest into the deaths, the ORR considered that none of them had yet been fully implemented.
Ms Kark, whose mother, author Nina Bawden, now 86, was badly injured in the crash, said: "Directors of the two companies should have been in the dock as individuals and they should have paid out of their own purses."
ORR rail safety director Ian Prosser said: "Today marks the end of a long process in which we have sought to gain a sense of justice for the families of the victims of the Potters Bar derailment."
He added that it was clear the rail industry still had "significant work to do" on safety.
Mrs Smith said: "There has been total disregard for the bereaved families. We have finally got our apology from NR. They should have put their hands up right away. That would have eased our pain."
Bob Crow, general secretary of the Rail, Maritime and Transport (RMT) union, said: "It is a scandal that those really responsible have got away with it."
Aslef general secretary Keith Norman said: "Surely those individuals responsible should be punished - not the travelling public."
Comments