Libbi's capture, announced last Wednesday, was described in the United States as "a major breakthrough" in the hunt for Osama Bin Laden and hailed by US President George W Bush as "a critical victory in the war on terror."
But according to European intelligence experts, Libbi was not the terrorists' third in command, as claimed, but a middle-ranker derided by one source as "among the flotsam and jetsam" of the organization, said the Times.
Bush had described him as a "top general" and "a major facilitator and chief planner for the Al-Qaeda network," while secretary of state, Condoleezza Rice said he was "a very important figure".
'Yet the backslapping in Washington and Islamabad has astonished European terrorism experts, who point out that the Libyan was neither on the FBI's most wanted list, nor on that of the State Department "rewards for justice" programme,' said the Times article by Christina Lamb and Mohammed Shehzad.
According to the Times, the Americans may have confused Libbi with another Libyan is on the FBI list - Anas al-Liby, who is wanted over the 1998 East African embassy bombings.
When The Sunday Times contacted a senior FBI counter-terrorism official for information about the importance of the detained man, he sent material on al-Liby, the wrong man.
"Al-Libbi is just a 'middle-level' leader," the article quoted Jean-Charles Brisard, a French intelligence investigator and leading expert on terrorism finance as saying.
"Pakistan and US authorities have completely overestimated his role and importance. He was never more than a regional facilitator between Al-Qaeda and local Pakistani Islamic groups," he said.
Although British intelligence has evidence of telephone calls between al-Libbi and operatives in the UK, he is not believed to be Al-Qaeda's commander of operations in Europe, as reported, the Times said.
'The only operations in which he is known to have been involved are two attempts to assassinate Pervez Musharraf, Pakistan's president, in 2003. Last year he was named Pakistan's most wanted man with a $350,000 price on his head,' it said.
No European or American intelligence expert contacted last week had heard of al-Libbi until a Pakistani intelligence report last year claimed he had taken over as head of operations after Khalid Shaikh Mohammad's arrest.
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According to the article, a former close associate of Bin Laden now living in London laughed: "What I remember of him is he used to make the coffee and do the photocopying,"
'Some believe al-Libbi's significance has been cynically hyped by two countries that want to distract attention from their lack of progress in capturing Bin Laden, who has now been on the run for almost four years,' the Times said.
One American official tried to explain the absence of al-Libbi's name on the wanted list by saying: "We did not want him to know he was wanted."
'Whatever his importance, al-Libbi is the sixth Al-Qaeda figure to have been caught in Pakistan, suggesting that the country is now the organisation's centre of operations,' said the Times.
The interior minister, Aftab Khan Sherpao, conceded that Bin Laden and his deputy might be hiding in a Pakistani city.
"But the capture of al-Libbi will have made them very apprehensive. Whether big fry or small fry, they're on the run, I can tell you that," the article quoted him as saying.