The Stockholm bomber was not on a list of 200 radical Islamists drawn up by Sweden's security service, officials have said.
Taimour Abdulwahab al-Abdaly, 28, was not identified as a potential risk by counter terrorism experts at SAPO.
The bomber, who lived with his family in Luton, killed himself and injured two others in the Swedish capital's shopping district on Saturday.
Malena Rembe, of SAPO's counter terrorism unit, said the agency downplayed the risk of terrorist attacks in a report.
The analyst added that it was previously thought radical Muslims aimed to support militants in Pakistan, Somalia and Afghanistan.
He said: "After Saturday's attempted attack, we can see that it also presents a serious threat against people in Sweden."
Detectives in Britain and Sweden continue to investigate whether Abdulwahab was supported by others or acted as a lone attacker.
They have been joined by seven explosives experts from the FBI who have studied improvised terrorist devices used around the world.
Officials said the botched bombing appeared "well-planned" and they are working on the assumption that he was helped by others.
One Swedish newspaper reported a second man accompanied him when he bought the white Audi he filled with gas canisters and set alight. Experts were also studying an audio recording in which he attacked Sweden's support of the war in Afghanistan.