Prosecutor Richard Whittam, QC, read statements made by people who saw the Fusilier's alleged murder near Woolwich barracks in south east London on May 22.
Two men, Michael Adebolajo, 28, and Michael Adebowale, 22, are on trial at the Old Bailey, London, and deny murdering Fusilier Rigby.They are also accused of attempting to murder a police officer and conspiracy to murder a police officer.
Saraj Miah, who was seen in a CCTV clip talking with a shopkeeper near the scene, said after Fusilier Rigby was run over, two armed men got out of the car. One of the two attackers pointed a gun at him when he told them not to kill the soldier. He said: "I thought the two black men with knives were going to kill him. I told them not to kill him. They did not listen."
One attacker slashed Fusilier Rigby's throat while the other stabbed him, the court heard. "The black man in the passenger seat with knives in both his hands stabbed the fallen man six times in his chest."
He described the man who had been driving the car walking around "as if nothing had happened".
Mr Miah said the two men then "threw the body on the left lane of the road". "I was very shocked by the incident," he added. "I could not sleep for two weeks."
Fusilier Rigby's widow Rebecca left the oak-panelled courtroom in tears as the statements were read.
Shopkeeper Ibrahim Elidemir shut himself, his girlfriend and two customers inside his store when he saw one of the attackers brandishing a knife after the crash, the court heard.
In his statement, he said: "The incident has affected me very badly. It made me feel very sad. I was very frightened and very scared at the time."
Amanda Bailey, whose statement was also read by Mr Whittam, described her shock at seeing the attack on the soldier, whom she said looked "like a young man coming home from college".
The trial continues.