Michael Adebolajo told police officers: "I am a Muslim extremist, this may be the only chance you meet one" moments after he had been shot following the Lee Rigby killing, at court has heard.
The Old Bailey was told how, Adebolajo, 28, spoke about the incident in Woolwich earlier this year.
"Your people have gone to Afghanistan and raped and killed our women, I am seeking retribution, I wouldn't stoop so low as to rape and kill women."
"I thank the person who shot me, because it is what Allah would have wanted. I love Allah more than my children."
Adebolajo also wrongly claimed that Fusilier Rigby, who was wearing a Help for Heroes hooded top, was in military kit when he was attacked, the court heard.
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He said: "My intention was never to hurt civilians. There were women and children around. My intention was to hurt military only. He was in his kit, in his uniform, coming in and out of the barracks."
Giving evidence, one of the male police officers, a rear passenger in the police car, said he felt he was "in the most urgent situation of his life".
The officer - known as E48 - fired from his seated position out of the window and hit one of the men, the court heard.
As the vehicle stopped, the other male officer, referred to as E42, left the car and saw Adebowale pointing a gun and shot him.
The female officer then also left the car and used her Taser on Adebolajo, the jury was told.
Jurors were shown pictures of the bloodied weapons that the men allegedly used, and the 9.4mm Dutch calibre revolver that was in their possession.
The court heard that Adebolajo handed a letter containing religious references to witness Ms Donnelly Martin.
It said: "Fighting Allah's enemies is an obligation", and went on: "Do not spend your days in endless discussion with the cowardly and foolish. It means that it will delay your meeting Allah's enemies on the battlefield. Sometimes the cowardly and foolish can be those dearest to you. So be prepared to turn away from them."
The handwritten note suggested "carnage reaching your town" was "simply retaliation for your oppression in our towns".
It said when the "heat of battle" came, "it is unlikely that any of your so-called politicians will be caught up in the the crossfire, so I suggest that you remove them."
The letter continued: "Muslims will trade with you on fair terms. Understand that the days of your international armed robbery are drawing to a close."
Jurors were also shown a video clip of Adebolajo speaking with blood on his hands, suggesting that the attack was "an eye for an eye".
The case continues.