Rachel Nickell was killed on Wimbledon Common in front of her young son
The Metropolitan Police force has rejected calls for an inquiry into errors made when police investigated the killing of Rachel Nickell in 1992.
On Thursday convicted killer Robert Napper admitted manslaughter on the grounds of diminished responsibility.
Police then apologised to Colin Stagg, wrongly accused of her murder in 1994.
They said more could have been done to catch Napper and prevent his further crimes but insisted the way murder is investigated has changed significantly.
Labour MP Keith Vaz had called for the police to review their procedures.
Rachel Nickell, 23, was stabbed 49 times as she walked on south-west London's Wimbledon Common with her two-year-old son Alex on 15 July 1992.
The police hunt for her killer led to Mr Stagg, from Roehampton, south-west London, who appeared on trial for murder in 1994.
But the case was thrown out after evidence from an undercover policewoman was ruled inadmissible.
Mr Stagg, who spent 13 months in custody, was awarded £706,000 compensation from the Home Office earlier this year.
On Thursday, the Met's Assistant Commissioner John Yates apologised to Mr Stagg.
He said: "It is clear he is completely innocent of any involvement in this case and I apologise to him for the mistakes that were made in the early 1990s."
He added: "We do say, however, that the way murder is investigated now has changed significantly from 16 years ago."
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.
Keith Vaz, chairman of the Home Affairs Select Committee, said: "We need to make sure whatever the technology involved that this kind of thing never happens again, so an internal review is extremely necessary."
But the Met told the BBC the case had been extensively reviewed already and lessons had been learned.
Speaking on Radio 4's Today programme, Peter Neyroud chief executive officer of the National Policing Improvement Agency, said: "The lessons of the Rachel Nickell case have been learnt - certainly critical ones about improvements to forensic work and improvements in senior investigating officer training.
"We have actually had legislation about one issue, which is the regulation of the covert activity.
"If you put those together and compare 1992 to what we've got now, I think Colin Stagg would have been ruled out pretty quickly due to the forensic evidence."
But barrister William Clegg QC, who has represented both Mr Stagg and Napper, told the programme: "It seems to me the problem with the Rachel Nickell case was that the police became overly reliant on the view of a purported expert in the form of the profiler.
"That is a failing that has happened since then on a number of occasions."
He called for courts to intervene more, as they do in the US, to make sure the expert's evidence "is not only relevant but also reliable".
An Old Bailey judge told Napper, 42, a convicted killer and serial rapist, he would be held indefinitely at Broadmoor high security hospital.
Mr Justice Griffiths Williams said: "You are on any view a very dangerous man."
Earlier, the court had heard psychiatrists believed Napper had paranoid schizophrenia and Asperger's syndrome at the time of the killing.
Napper admitted the killing of Samantha and Jazmine Bissett
He was questioned in December 1995 about Miss Nickell's killing, but denied involvement.
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 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.
He was interviewed again in Broadmoor in 2006, but again did not own up to the crime.
In 1989, officers failed to question him after his mother rang a local police station to say he had confessed to a rape.
Napper was also questioned about a series of sex attacks in 1992, but was wrongly eliminated.