Giving a statement to the House of Commons after the figures were released, Lammy said: "I'm clear that we must bear down on these numbers, which are symptomatic of a prison system under a horrendous strain."
He told MPs the number of frontline prison officers had been cut by a quarter between 2010 and 2017, leaving fewer experienced staff.
"Unsurprisingly, mistakes happen in those circumstances," he added.
Lammy said the prison release process needed "a radical overhaul" and "only technology will fix this issue over time".
He set out a number of actions the government was taking, including:
It comes after the government launched an independent review of accidental releases, which is expected to report back in February next year.
In his statement, Lammy also gave more details about three prisoners released by mistake who are still at large.
The first was in jail for failure to surrender to the police and was released in error in December 2024.
The second was in prison for a drug offence and released in error in August 2024, while the third was in prison for aggravated burglary and released in error in June 2025.
One is a foreign national offender and the other two are British.
Lammy said His Majesty's Prison and Probation Service was also investigating a further case of a potential release in error on 3 November, who may still be at large.
Conservative shadow justice secretary Robert Jenrick accused Lammy of presiding over "a complete and utter farce", saying he had "literally lost track of how many prisoners he's lost".
"The public are being put at risk," he said, adding that Lammy must "get a grip or go".
Jenrick, who had called for the latest figures to be released, said Lammy had to be dragged "kicking and screaming" to make them public.
He sought to blame Labour's early release scheme for creating "confusion" and contributing to the rise in prisoners being released by mistake.
The emergency scheme, which was introduced after prisons almost reached full capacity, allows some inmates to be released after serving 40% of their fixed-term sentence, rather than the usual 50%.
However, Lammy said the move was needed because the Conservatives had not built enough extra prison places when the party was in government.