Relatives of Barnaby Webber, Grace O'Malley-Kumar and Ian Coates have made a formal complaint about the Panorama episode.
They say it contained inaccuracies, was too sympathetic towards the knifeman's family and they were refused a preview screening.
Barnaby's mum Emma said: "We believe what the BBC produced is a very imbalanced documentary - it's shameful, cold, ill-judged, arrogant and thoughtless."
Their loved ones were butchered when Valdo Calocane, 32, went on the rampage through the streets of Nottingham in June last year.
He knifed Barnaby and Grace, both 19, as they returned from a night out in the early hours, then stabbed school caretaker Ian, 65, and stole his van, crashing it into three people, who suffered serious injuries.
The victims' families were further traumatised when they learned police had failed to detain Calocane when he attacked a cop a year before.
And they were devastated when prosecutors dropped murder charges.
Instead, in January, Calocane admitted manslaughter and received a hospital order because of his mental condition. Last night Emma, speaking on behalf of all three families, said watching the BBC's treatment of the case had made their trauma even worse.
The BBC only informed them about the show after they had already filmed it and a fortnight before it was due to be broadcast.
Panorama's The Nottingham Attacks: A Search For Answers aired last month and boasted it would consider "big questions" on the case.
But Emma said: "We were not considered or consulted at any point to advise that this was being made."
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