David Merritt took to social media to hit out at the prime minister, claiming he used his 25-year-old son's death to "make political capital" during the BBC Election Debate with Labour leader Jeremy Corbyn.
Writing on Twitter on he said: "Wake up Britain, this man is a fraud.
"He's the worst of us, and he's taking you for a ride."
He also accused Mr Johnson of making false claims and said Mr Corbyn "spoke the truth".
Cambridge University graduates Jack Merritt and Saskia Jones, 23, were attacked by Usman Khan on Friday, November 29, during a prisoner rehabilitation event at Fishmongers' Hall.
Khan attacked five people, including the graduates, armed with two kitchen knives and wearing a fake suicide vest.
He was tackled by members of the public on London Bridge and then shot dead by police at point-blank range.
During the BBC debate, the two party leaders were asked about balancing the needs of security against human rights in the wake of the terror attack.
Mr Corbyn said: "What happened on the streets of London was utterly appalling and I was very moved by what Jack Merritt's father said about what his son was trying to do.
"That he wanted a society where you did address the huge problems where somebody committed awful acts; of course you must imprison them, of course you try and rehabilitate them if you can."
Mr Johnson said: "I have huge sympathy for Mr Merritt and the families of both victims and it was an absolutely terrible thing.
"But I still think it's wrong that someone like Usman Khan, who was sentenced to 21 years or 16 years plus five on licence, should have been out automatically on eight years."
But Mr Merritt said on Twitter that there was no justification for cutting the early release tariff and claimed it was just trying to "look tough".
He added: "There is no justification at all for cutting the early release tariff from a half to a third of sentences for all sentences over four years that carry a maximum life sentence - that's just trying to look tough on the backs of other prisoners' suffering.
"If prisoners have engaged with rehabilitation and turned their lives around, why should they be punished for what Khan did?"
Speaking to reporters in Reading, Liberal Democrat leader Jo Swinson said: "I'm heartbroken for Jack Merritt's father for what he is going through, which I can't even begin to imagine the intensity of that grief.
"And that he has something to say and he has really clearly said he did not want politicians to politicise his son's murder.
"And the very least Boris Johnson could have done was to listen to a grieving father and respect his wishes. And instead, he has done the opposite."
A GoFundMe page set up by Jack Merritt's friends and supported by his family has raised nearly £12,000 in under 24 hours.
Reporting by PA.