"We understand the upset. We understand the disagreement. But we have to do what is right in terms of our legal system, that is what we are duty-bound to do," he said.
"No-one, I think, seriously believes that we made any other decision except for the right reasons," he added.
Megrahi, 57 - who is terminally ill with prostate cancer - was freed last week by Mr MacAskill, on compassionate grounds.
He was given a life sentence for killing 270 people in the 1988 Pan Am Flight 103 bombing, and served 10 years before being released.
The Libyan returned home to Tripoli to jubilant scenes that included people waving Scottish flags.
Labour's Jack McConnell, who preceded the SNP's Alex Salmond, said it was up to the Scottish Parliament to take action to repair some of the "damage" caused by Megrahi's release.
"The way in which the decision has been made and the decision itself have damaged the reputation of the Scottish justice system," he told the BBC.
"Much more significantly it's also damaged the reputation of Scotland internationally."
Meanwhile UK Prime Minister Gordon Brown is facing fresh calls to give his opinion on the Libyan's release.
On Saturday, Libyan TV showed pictures of Col Gaddafi meeting Megrahi and praising "my friend" Gordon Brown and the British government for what he said was their part in securing his freedom.
Jack McConnell said that the scenes in Libya had "damaged the reputation of Scotland"
Senior ministers have stressed the issue is a matter for the devolved Scottish Government alone.
Shadow defence secretary Liam Fox told the BBC: "We know what David Cameron thinks about it... we know what the former and current first ministers of Scotland think, we know what everyone thinks except Gordon Brown.
"When the going gets tough, Gordon Brown disappears, it's the story of his political career."
While no opinion has been issued by Mr Brown, the Scottish Government did seek legal advice from UK Foreign and Commonwealth Office (FCO), ahead of the decision.
The FCO advised that there was no legal barrier to transferring the prisoner, and minister Ivan Lewis wrote: "I hope on that basis you will now feel able to consider the Libyan application."
But a FCO spokesman said it was "absolute rubbish" to suggest the letter had in any way provided encouragement to let Megrahi return to Libya.
As the debate intensified, Libya rowed back on suggestions that Megrahi's repatriation was part of a trade deal with Britain.
Saif al-Islam Gaddafi, the son of Libyan leader Colonel Gaddafi, reportedly told a TV station that Megrahi's case was "always on the negotiating table" during trade talks, but his spokesman said the comments had been taken out of context.
Business Secretary Lord Mandelson dismissed suggestions of a deal as "offensive".
In a scathing letter to Mr MacAskill, chief of the US Federal Bureau of Investigation Robert Mueller said the action made a "mockery of the rule of law" and "gave comfort to terrorists".
Mr Mueller - who played a key role in investigating the 1988 atrocity - said: "Your action in releasing Megrahi is as inexplicable as it is detrimental to the cause of justice."
The devolved Scottish Government can make decisions on Scottish justice independent of Westminster, but foreign affairs for the whole of Britain are still dealt with by the UK government.
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