He has made the claim despite the murderer being ordered to spend a minimum of 37 years behind bars at the age of 69.
Sinclair, who killed teenagers Christine Eadie and Helen Scott after a night out at the World's End bar in Edinburgh in 1977, died in Glenochil prison in March at the age of 73.
His death came after he was given the longest sentence ever handed out by the Scottish courts in 2014.
Mr Kerr said: "The fact he died behind bars was an accident not by design and our criminal justice system should simply not be countenancing that."
Community Safety Minister Ash Denham cited the case of Sinclair as showing how judges in Scotland can impose sentences that will mean an offender dies behind bars.
But Mr Kerr, who is planning to introduce a member's bill to Holyrood to introduce whole life sentences in Scotland, argued: "The incontestable fact is this - Scottish courts cannot by law guarantee that the worst criminals will not be let back on to our streets."
Under the current system, he argued judges lack the power to ensure the worst criminals are never released from jail.
The Conservative MSP said: "We are told the Scottish courts already have the power to set a punishment part that is longer than the rest of an offender's life - if the criminal happens to be elderly or terminally unwell, yes.
"But that turns on chance, it cannot be designed."
He added: "The longest punishment part that has ever been handed out by a Scottish court is 37 years.
"Even that, the most extreme example is not the rest of your life if you are in your 20s."
Mr Kerr told MSPs: "Some offenders commit crimes that are so appalling that the risk of reoffending should be removed altogether.
"It is time to protect Scotland's communities by removing the worst criminals from society for good."
Ms Denham said: "Judges have the powers that they need to appropriately sentence the most serious offenders that come before the High Court.
"The Appeal Court has confirmed that Scottish courts can impose a punishment part that exceeds the rest of an offender's life.
"For example, Angus Sinclair, who was convicted of the World's End murders in 2014, he was sentenced to life imprisonment with a punishment part of 37 years.
"This meant that he would not have been able to apply for parole until he was 106-years-old."
She added: "There are other examples of people convicted of the very worst crimes being given punishment parts of 30 years or more."
Other MSPs branded Mr Kerr's proposed bill a "stunt" and "political posturing"
Labour's Pauline McNeill said: "This bill is a meaningless stunt.
"Judges can extend the punishment beyond the likely remainder of a prisoner's life. It has happened on numerous occasions."
Liberal Democrat Liam McArthur said it was of "political posturing rather than a serious attempt to reform sentencing to better meet the needs of victims and their families", while Green MSP.
John Finnie said the Conservative was "pandering to a certain audience".
Mr Kerr hit back at those suggestions, saying: "This isn't a stunt, I've been working on the guts of it for the last two years.
"A stunt is not something you pull out after two years of very difficult work."