Dave Merritt said "instead of seeing a tragedy", Mr Johnson "saw an opportunity and he went on the offensive".
In his first TV interview since the tragedy, he said he felt he had speak up when he saw the Prime Minister was politicising the attack by blaming it on the Labour Party.
He told Sky News: “What was required was just a dignified approach whereby the politicians would express their regrets, express their condolences to the people affected, and would then get on with campaigning in the election. It wasn’t an election issue.
“Where most of us were watching this and seeing a tragedy unfolding in front of our eyes, instead of seeing a tragedy Boris Johnson saw an opportunity and he went on the offensive.
“He saw an opportunity to score some points in the election – he immediately said ‘oh this is Labour’s fault, they allowed this to happen, they had this early release policy’ and so on.
“At that point… well I had to say something.”
Mr Merritt added that there was “no attempt” to contact the family from Downing Street or Mr Johnson.
He said: “The only contact we had was that the police liaison officer said to us ‘I’ve been asked if you would like to meet Priti Patel for her to express her condolences’. We just said no thank you.”
25-year-old Jack and fellow Cambridge graduate Saskia Jones, 23, died after being stabbed by terrorist Usman Khan during a prisoner rehabilitation event at Fishmongers' Hall on November 29.
Mr Merritt insisted he does not blame the police or intelligence services for not being able to stop the attack, as he revealed Jack had known and tried to help Khan as part of his work.
He said: “The only person responsible for what he did is him (Usman Khan), so I’m not going to start lashing out and saying ‘somebody should have stopped this, somebody must be responsible for this’.”
He added: “I don’t feel angry about what happened, I feel bereft and very, very sad.
Mr Merritt said the "hardest part" of the tragedy was having to tell Jack's brother of his death.
He said: "He didn't know. We didn't want to tell him over the phone and we didn't want anybody else to tell him so we went and got him and we had to tell him that his brother died. Which was probably the hardest thing I’ve had to do."
Referring to his son, he added: “He was an exceptional person, probably more exceptional than I realised before this happened.”
Khan attacked five people, including the graduates, armed with two kitchen knives and wearing a fake suicide vest before he was tackled by members of the public on London Bridge and then shot dead by police at point-blank range.