Parliament's Intelligence and Security Committee said that if British spies had known of Michael Adebowale's declaration, "there is a significant possibility" they could have prevented the May 2013 murder.
But the online exchange was only discovered after Adebowale and Michael Adebolajo killed Fusilier Lee Rigby.
The lawmakers concluded that spy agencies had made mistakes, but that with the knowledge they had at the time they "were not in a position to prevent the murder."
Adebolajo was arrested in Kenya in 2010; authorities said he was trying to travel to Somalia to join the militant group al-Shabab.
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The committee was critical of Britain's foreign intelligence agency, MI6, for waiting four months before opening an investigation into Adebolajo after he returned.
The report was highly critical of US-based communications companies such as Google, Twitter and Yahoo for failing to report extremist content or comply with requests from British agencies to hand over information.
Adebolajo and Adebowale are serving life sentences for murdering 25-year-old Rigby, who was run down with a car before being attacked with knives.