Mr Jenkins, 52, said he had not given "a second's thought" to the rejection by the Ministry of Justice (MoJ) of the reported £500,000 claim his legal team submitted.
And he said he believed receiving compensation would not have convinced everyone that he was innocent of murdering 13-year-old Billie-Jo Jenkins.
He said he had not appealed against the MoJ's refusal, saying the most important thing was "that the investigation" into finding her killer "doesn't die".
Speaking to the Press Association, Mr Jenkins said his focus now was to see her killer face justice 13 years after she was bludgeoned to death at the family home in Hastings, East Sussex.
Speaking about Billie-Jo, he said he treated her like one of his own daughters and that he will never get over her death.
He said he "always remains hopeful" that her murderer will be apprehended, and gains hope from other cases which went unsolved for many years.
Speaking for the first time about his compensation refusal in 2008, Mr Jenkins said: "I'm not appealing the decision because it's not important.
"The most important thing for me is that the investigation doesn't die and that Sussex Police continues to look for leads.
"I can think of a number of things that could be done and I have requested them. That's what's important.
"It's something the legal team simply put in for because I'm a miscarriage of justice.
"I haven't given it a second's thought for the last two years. It's simply not important to me.
"I'm not living in a hostel. I'm not living on the street like some unfortunate miscarriage of justice and so it really isn't important."
Mr Jenkins went on: "There is only one thing that is important and that is to find the person who murdered Billie.
"I'm no different to any other parent. I thought of Billie, and continue to think of Billie, as my daughter.
"Invariably the press say 'foster father', but she was a daughter as like any father who is still, in many ways, coming to terms with everything that has happened.
"I will never get over it. Would any father get over the fact that his daughter has been murdered? Of course they wouldn't and I'm no different.
"I would never get over it and as far as my priorities are, it is that the person who murdered Billie is found, apprehended and convicted."
He added: "The hardest thing to accept is that Billie isn't alive anymore and that I have lost a child, and in losing her there are so many other things.
"The years I spent in prison paled into insignificance when I think of the loss of her life.
"Nothing compares."
Of his hopes that her killer will be caught, he added: "I always remain hopeful that this is the case.
"There may be little point in me saying, 'Well, no I don't' because then I would hold up my hands and simply say there is nothing we can do here, but I'm not prepared to do that. And anyway the facts and other evidence of other cases where you have particular offences which go unsolved for many years and then they are solved, so I'm still hopeful."
Billie-Jo was found in a pool of blood with head injuries inflicted by a metal tent peg on the patio of the family's large Victorian home in Lower Park Road, Hastings, on February 15, 1997.
Mr Jenkins, at the time headteacher-designate at all-boys William Parker School in Hastings, maintained his innocence and insisted Billie-Jo must have been killed by an intruder while he visited a DIY store.
In 1998 he was convicted at Lewes Crown Court of murdering her and jailed for life. But he had a retrial in 2005 after successfully appealing.
However, the jury failed to agree a verdict and a second retrial ended the same way in 2006, allowing him to walk free.
Following the killing, his ex-wife, Lois, emigrated to Tasmania with their four daughters, who chose to have no contact with their father.
Mr Jenkins, who now lives in Hampshire after marrying Tina Ferneyhough, said: "I haven't seen my girls.
"When parents divorce, sometimes bitterly, estrangements take place.
"I'm hopeful that everything that has happened over the past few years, particularly with Billie's murder, to say it was traumatic on each of us is an understatement and is going to take many more years before people come to terms with what has happened.
"But I will never be able to get over it. Never. My life will never be the same again.
"How can it be? And if that's the case for me, it will be the case for other people."
Asked whether he believed receiving compensation would free him of suspicion in most people's minds, he replied: "No, I don't.
"People who want to believe guilt because of their own prejudices will continue to always do so. Those who have an open mind will take another view.
"The majority of people, of course, when they make judgments on any miscarriage of justice weren't at the trial and weren't at the appeal.
"Most people weren't there so they have no idea what the facts of the case are other than what they read in a newspaper."
Campaigners for Mr Jenkins yesterday condemned a statement from the MoJ which said the Appeal Court made clear compensation should be paid when someone has been shown to be "clearly innocent".
A response posted on the Justice for Sion Jenkins website called it an "insidious" remark, and added: "In which universe does 'not guilty' mean 'not innocent'?"
Responding to the statement, Mr Jenkins said: "The MoJ would say that. It's the standard line."
He went on: "From my perspective, my interest is more in miscarriages of justice generally.
"It seems to me quite bizarre that as we live in a compensation-fuelled age that you can take a man or woman and wrongfully incarcerate them for many years and when they come out you compensate them in no way.
"I always believe before an individual went to trial that an individual was innocent until proven guilty. I always thought that was important.
"When someone goes through the criminal court, it is the responsibility of the prosecution to find guilt. From that point, if the conviction is quashed then that's it.
"For any Ministry of Justice to put another demand on any miscarriage, 'Sorry, you have now got to prove innocence', is unrealistic but it is a clever way of making sure that you don't have to pay out compensation."
In his book, The Murder of Billie-Jo, Mr Jenkins said he identified a possible new suspect for her killing.
He said he spoke to someone he thought was a dark-haired, plain-clothed police officer in his hallway in the confused hour after Billie-Jo was found bludgeoned to death.
Today Mr Jenkins, who is studying for a doctorate at the University of Portsmouth, said: "Within the whole case there are a whole variety of anomalies and the fact is that I saw this person and I don't know who they were.
"People said it seems funny that you are mentioning it now but of course I mentioned it in a witness statement three days after the murder and continued to mention it.
"The fact was in my main witness statement. I don't know who that person was, so that's another lead and there are other leads that I think should be looked at.
"For example, whoever murdered Billie used a long metal tent peg. Has the tent peg been DNA'd? That is another avenue.
"I'm not stating that I know anything but I raise these things in the hope that people, particularly the police, will give them due diligence and accord.
"I don't want avenues closed down. It's hard enough trying to solve a crime 13 or 14 years after the event without closing down particular leads.
"If they have looked at it, and if it was found, for example, that the person I had seen was a police officer and I have got the times mixed up then I would be happy to accept that.
"But if it is the case then let's go on to another lead. I don't think it's the time for refusing any new bit of evidence because I want to find the person who killed her."
Mr Jenkins said he has been back to Hastings since being freed and recalled the happy memories he holds of the East Sussex seaside town before the death of Billie-Jo.
"The fact is that whilst there, the years before, with all my family, we were very happy and I have got very fond memories and still have friends in Hastings," he said.
Sussex Police have said the Billie-Jo murder case remains "unresolved" but they continue to actively pursue any new lines of inquiry which emerge.
Of the future, Mr Jenkins said: "We just press on. Sussex Police say it is unresolved and I agree it is unresolved. It won't be resolved until they find a culprit.
"But my campaign won't stop and I will simply keep on pressing on.
"I take heart from the many other campaigners for justice in some way. Although it has been a very long journey for them, they have reached their destination.
"I will simply keep on pressing on. I don't need to work hard to do that.
"I don't need to wake up in the morning and think, 'Well, is it time to put this all behind me and just simply get on with my life?'
"That will never happen."
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