Shadow home secretary Diane Abbott said Mrs May, who was home secretary before becoming PM, had allowed officer numbers to fall in recent years.
The Conservatives said Ms Abbott had "dangerous" views on protecting the public.
Armed police numbers have increased, a Conservative spokesman added.
Following the London and Manchester terror attacks, security is featuring heavily in the final days of campaigning before Thursday's general election.
Labour has been targeting cuts to the Home Office's policing budget - the Conservatives have rejected the criticism and a former terrorism law watchdog said linking the cuts to terror attacks was a "completely misleading argument".
Speaking to the BBC, Ms Abbott said it was "concerning" that action was not taken when one of the London attackers - 27-year-old Khuram Butt - was known to the security services.
She said this reinforced the need for an increase in community police officers.
Latest figures show that between September 2010 and September 2016, police workforce numbers in England and Wales fell by 18,991, or 13%.
Ms Abbott said police numbers had fallen "on Theresa May's watch" despite warnings from the Police Federation and HM Inspector of Constabulary.
"So she should really consider how much of this goes back to her door and the decisions that she took," she said.
Asked how much of a connection there was between Saturday's attack and the cuts to officer numbers, she added: "She does need to explain why she thought it appropriate to watch police numbers go down by 20,000 when she had so many warnings from so many people that this was putting people at risk.
"Clearly the people responsible for these horrific terror attacks are the bloodthirsty and depraved terrorists but Theresa May has to take responsibility for letting austerity damage her ability to keep us safe."
Speaking in a special general election edition of Question Time, Lib Dem leader Tim Farron said cuts to police numbers had "not made us safer".
But Lord Carlile, the former independent reviewer of terrorism legislation, told the BBC cuts in community policing were "nothing to do with terrorism", saying "nobody in the security services is complaining about their funding"
Following the London attack, Mrs May said "things need to change" in the fight against terrorism, calling for more to be done about online extremism and for a review into whether security services needed extra powers.
Speaking to BBC Newsbeat, she defended her record, saying she had given the police extra powers to deal with terrorists and that there had been an increase in the number of people reporting suspected extremists to the authorities.
The Conservatives described Labour's criticism as "desperate stuff", saying the security services had been boosted with extra officers.
"Diane Abbott's views on keeping us safe are as dangerous as she is hopeless under pressure," a spokesman said, saying she had "voted against every piece of security legislation designed to keep us safe".

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Fresh from collecting a fourth career gold medal at London 2012, Ainslie is now concentrating on making a challenge for the 35th version of the series.
The 34th America's Cup, to be held in San Francisco in September 2013, will come too early for the Briton.
"I've had some America's Cup experience in the past and I would really love to be part of a winning team in the future," said Ainslie.
"As a kid my main two goals were the Olympics and the America's Cup."
He will sail a catamaran under his Ben Ainslie Racing (BAR) banner, with JP Morgan announced as the main sponsor for the team, and will enter the upcoming America's Cup World Series, which starts in San Francisco on 21 August.
"We started a new team, JP Morgan BAR, which will take part in the America's Cup World Series," he said.
"It will take part in this coming series and the one after, which is really a great opportunity for us to build this team up.
"The next America's Cup is in 2013 and we want to try and build this team up for the World Series so we can be a proper challenger for the America's Cup post-2013."
Ainslie won his fourth Olympic gold in a row by coming home first in the Finn class at Weymouth, a victory that makes him the most decorated Olympic sailor in history.
Labour has accused Theresa May of "letting austerity damage her ability to keep us safe" as it continues its attack over police cuts.
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Olympic hero Ben Ainslie has outlined his plans to win the America's Cup.