Mr Stagg, 45, spent 13 months in custody. This year, he was awarded £706,000 compensation from the Home Office.
After Thursday's trial Assistant Commissioner John Yates apologised to Mr Stagg for the "mistakes made".
In a statement, Ms Nickell's parents Andrew and Monica said: "The greatest loss is your future.
"All the things that any family hopes for and expects are completely smashed. There will be no daughter to talk to in our old age, no grandchildren to love and admire.
"At a stroke all this has been removed."
Question marks still hang over the original investigation and the missed opportunities to catch Napper, who went on to kill another young mother and her daughter.
Napper was questioned in December 1995 about Ms Nickell's killing and denied involvement.
Colin Stagg on his ordeal
He had been sent to Broadmoor secure hospital two months earlier for raping and killing Samantha Bissett, 27, and her four-year-old daughter Jazmine in an attack in Plumstead, south London in November 1993.
A tiny particle of Napper's DNA was picked up when Miss Nickell's body was swabbed soon after her death.
But it was too small to be analysed until recent advances made it possible. A match to Napper was confirmed in 2004.
The former warehouseman, who lived near Miss Bissett, was interviewed again in Broadmoor in 2006, but again he did not own up to the crime.
Police investigators admit that a series of failings meant Napper was not caught sooner.
Officers failed to question him after his mother rang a local police station in 1989 to say he had confessed to a rape.
The officer she spoke to could not match up details of the offence with any rape which had been reported.
Napper was also questioned about a series of sex attacks in 1992, but was wrongly eliminated.
"We have been absolutely honest about this to their family and we have told them that we deeply regret that this happened and have apologised to them," Commander Simon Foy said outside court.
For more on the story watch Innocent: The Colin Stagg Story on BBC One at 10.30pm tonight.
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