Seventeen people, all of them civilians, were killed when a car bomb exploded near a Shia shrine in the south of the capital.
Al-Hussein said the aim of the attack, the deadliest to hit Syria in about a dozen years, was to "harm the [country's] regime".
The men said they raised finances for the attack by carrying out several armed robberies.
They said the car used in the bombing had been stolen from an Iraqi.
Last November, the Lebanese army fought a 15-week battle with Fatah al-Islam in a refugee camp at Nahr al-Bared near Tripoli.
More than 400 people were killed in the fighting, including 168 soldiers.
Shaker al-Abssi, the leader of Fatah al-Islam, fled the army's siege of the camp and vowed to launch revenge attacks in Lebanon.
Those shown on the Syrian television programme said that they had not heard of al-Abssi since July.