The shadow home secretary accused South Yorkshire Police Force of covering-up officers' failures in a bid to prevent the truth of how 96 Liverpool FC fans were killed coming to light.
Mr Burnham added that decades of lies by police had caused "incalculable" damage to families who have fought for 27 years to discover how their loved ones died and who was to blame.
"This inquest has today delivered justice, and I would say next must come accountability," the Leigh MP told BBC Radio 4's The World at One.
"People have lied down the decades and those lies have cause terrible harm. It was stuff said in the aftermath of the biggest stadium disaster - Liverpool's moment of greatest grief.
"The damage that those lies did was incalculable and that’s why I would say there has to be accountability and there have to be prosecutions.
"Individuals must be held to account for their actions, because nobody at this point has been held to account from the South Yorkshire Police, so part of justice is accountability and that is why I say prosecutions must follow this verdict."
The shadow home secretary was speaking hours after a ruling that found the 96 Liverpool fans crushed to death at Sheffield Wednesday's Hillsborough stadium had been killed "unlawfully", and that police planning "caused or contributed" to the situation.
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Mr Burnham said that justice for those killed in the 1989 tragedy had finally been achieved, following the conclusion of the longest jury case in English legal history.
But he impressed the urgency of following up today's inquest with prosecutions.
"Why did it take 27 years? It took 27 years because the police force tried to deflect the blame off themselves and on to the Liverpool supporters," the Labour MP said.
"This police force has consistently - for the last 27 years - put protecting itself ahead of protecting those hurt by the horror of Hillsborough.
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"That is what has happened, and the fact that they decided to contest this inquest, to throw around these allegations again, meant that it took a year or more longer than it should have done and tens of millions of pounds been spent on this.
"How can public money be given in such quantities to the telling of lies in a court room by a police force - I should say by retired officers, to make that distinction."
The Crown Prosecution Service has confirmed it will begin the process of considering whether criminal charges should be levied.