The UK government has said legislation may be brought in to stop the Human Rights Act endangering public safety.
There was concern over the way the act was working, Lord Falconer said
The Lord Chancellor said the act would not be scrapped but could be amended in parliament to ensure its application was not "distracting" officials.
Lord Falconer told the BBC's Sunday AM cases like that of rapist Anthony Rice, who killed a woman while on parole, raised concerns over the law.
Human rights groups said the current concerns were not a fault of the act.
"Amending our human rights act because of gross public service failures is like handing a repeat burglar the key to your house," said Shami Chakrabarti, director of campaign group Liberty.
"Without the act, ordinary people in Britain would have precious little protection from maladministration."
The European Convention on Human Rights was incorporated into UK law in 1998 through the Human Rights Act.
Lord Falconer said the government did not intend to pull out of the convention - a condition of EU membership.
But he said it is considering a programme of education and training or "if necessary" new legislation to make sure it is not wrongly interpreted.
He said there was a "real concern" about the way the Human Rights Act was operating and there needed to be "political clarity" that it would have no effect on public safety issues.
"This is not about an attack on the judges, this is about making clear in particular areas - like example the release of prisoners who might be a danger to society - that public safety comes first," he said.
"We need to be absolutely clear that human rights does not in any way reduce people's public safety."
The report into Anthony Rice's murder of Naomi Bryant in Winchester last year said officials had considered his human rights above their duties to the public.
It recommended the "top priority focus" in future should be on public protection.
The act was also cited when the High Court ruled nine Afghan asylum seekers who hijacked a plane could stay in the UK.
The government was criticised by a judge for failing to implement a decision that the men could not be deported as their lives were under threat.
BBC political correspondent Terry Stiastny said some ministers were worried about the public's perception of the act and possible "over interpretation" by officials.
But she added that new legislation was still only a "distant possibility".
Conservative leader David Cameron has pledged to reform, replace or scrap the Human Rights Act if he is elected as he said it is undermining the UK's ability to deal with foreign criminals.
Shadow home secretary David Davis told Sunday AM concerns over the act had been raised by the Conservatives in 1998.
"Tories are not against human rights but we think the way the government has done it has led to disasters."
Liberal Democrat constitutional affairs spokesman Simon Hughes said: "The answer is to seek better collective protection, not rip up human rights obligations which have stood the test of time and are important guarantees for the rights of us all."