The parents of Reeva Steenkamp expressed anger and disbelief on Friday after Oscar Pistorius was formally acquitted of their daughter's murder, insisting: "Justice was not served."

Amid growing discontent in South Africa at the verdict, the Steenkamps criticised judge Thokozile Masipa for being too lenient on the athlete, who was instead convicted of culpable homicide, the South African equivalent of manslaughter, and granted bail.

"This verdict is not justice for Reeva," her mother, June Steenkamp, told NBC News. "I just want the truth."

Steenkamp, a 29-year-old model and law graduate, died in a small toilet cubicle when Pistorius shot her four times through the locked door just after 3am on Valentine's day last year. The court heard how his hollow tipped bullets opened and mushroomed on impact, tearing through her flesh and killing her almost instantly. He claims he mistook her for an intruder, a version that the judge accepted.

She died a "horrible, painful, terrible" death, June added. "He shot through the door and I can't believe that they believe it was an accident."

Although Pistorius looked relieved at the judgment, he will return to court on 13 October for a sentencing hearing and could face up to 15 years in jail, though a shorter jail sentence of perhaps five years is considered more likely.

June Steenkamp told NBC News: "I really don't care what happens to Oscar. It's not going to change anything because my daughter is never coming back. He's still living and breathing and she's gone, you know, forever."

Jacqui Mofokeng, a spokeswoman for the African National Congress women's league, who supported the Steenkamps in court, said: "They are saddened by the verdict. It's like they're mourning Reeva again. Emotions are high. Some of the family were crying when the verdict was given."

After a six-month trial that saw the double-amputee athlete sob, moan and vomit into a bucket, on Friday the high court in Pretoria was besieged by camera crews, photographers and reporters from all over the world. Yet Masipa's final verdict came in low-key circumstances, with her decisions having already become clear during the reading of her judgment.

"Mr Pistorius, please stand up," she instructed the accused. Wearing a dark suit, Pistorius rose in the dock and stood ramrod straight, his hands folded in front of him, and showed little emotion as the judge read her final verdict.

"Having regard to the totality of this evidence in this matter, the unanimous decision of this court is the following: on count one, murder … the accused is found not guilty and is discharged," Masipa said. "Instead he is found guilty of culpable homicide."

There was little instant reaction from members of the Pistorius and Steenkamp families sitting on the front row. But when the court adjourned for lunch, June Steenkamp could be seen shaking her head and putting an arm around another family member, while Steenkamp's friend Gina Myers openly wept.

Meanwhile Pistorius's estranged father Henke offered him a smile and comforting hand. The athlete seemed to acknowledge him but quickly ended the encounter. The mood was sombre rather than celebratory.

Pistorius, 27, was also found not guilty of illegally possessing ammunition, and firing his weapon through a car sunroof. But he was convicted of negligence relating to an incident in which a gun went off in his possession at a restaurant where more than 200 people were present in January last year.

Masipa turned down an application by prosecutors to refuse bail. It means the sprinter, nicknamed the "blade runner" because of his prosthetic limbs, will continue to live with his uncle Arnold in Pretoria, his residence for the 18 months since the shooting.

Arnold Pistorius said the family were grateful to the judge for finding the sportsman not guilty of murder. "It's a big burden off us, off our shoulders and Oscar.

"We always knew the facts of the matter and we never had any doubt in Oscar's version of this tragic incident. We as a family remain deeply affected by the devastating tragedy … It won't bring Reeva back, but our hearts still go out for her family and friends."

Across South Africa, there was consternation at the judge's verdict. Many people took to radio phone-ins and social media to vent their bewilderment and the hashtag #Justice4Reeva quickly started trending on Twitter. Some suggested that Pistorius had been given exceptional treatment because of his celebrity, wealth and race.

Eusebius McKaiser, a talkshow host on the Johannesburg-based radio station Power FM, said he had received hundreds of calls and text messages during his morning show and "99% of them think it was a mistake".

McKaiser, an author and columnist, took the same view: "She should have found him guilty of murder. There are good prospects for the state to appeal on a point of law. The higher court might even rebuke her for getting it wrong. The mistake she made really was elementary."

The judge was wrong to use details of Pistorius's conduct after the killing, such as praying to God to save Steenkamp's life, as evidence of his intention when he pulled the trigger, McKaiser added. "That's the bit I deem to be embarrassing and not just wrong. It doesn't matter what happened afterwards. These facts are irrelevant to the case."

Lawyers also joined the criticism. Martin Hood, an attorney specialising in firearms offences, said: "There has been a widespread expression of outrage across the board. There are many people in the legal profession who believe she got it wrong. It has met with a lot of disappointment in the court of public opinion, including on the part of gun owners."

He added: "I would be bitterly disappointed and angry if I was Reeva Steenkamp's family."

The national debate quickly drew comparisons to Molemo "Jub Jub" Maarohanye, a black rapper sentenced to 20 years in prison for murder after crashing into a group of boys while drag-racing through the streets of Soweto.

Trevor Noah, one of South Africa's leading comedians, tweeted: "I'm very confused. Jub Jub raced a car high and was found guilty of murder, Oscar went to fetch a gun but he gets less time?"

Another Twitter user, "prince akeem", posted: "Jubjub didn't even mean to kill those kids but he got murder but pointing a gun and shooting four times is an accident."

The conviction of culpable homicide can bring a maximum prison sentence of 15 years, although legal experts pointed to five years as a guideline. The prosecution gave no indication of whether it planned to appeal.

The National Prosecuting Authority said: "We respect the court decision to convict the accused on culpable homicide, which is in fact a serious crime. We are, however, disappointed that we were not successful in securing a conviction on the original charge of premeditated murder.

"NPA will await until the matter is concluded and will then comment on any further legal steps that might be envisaged."