Speaking to Sky News after her win, Ms Forbes said: "I have no issue with any community, I think antisemitism is abhorrent.
"I actually liked a video of children praying about the atrocities that had happened in New Zealand and I hadn't paid much attention to the text above it and I apologised for that.
"I'm really sorry and I just hope that people will understand that I don't have a bad bone in my body towards any race of people and antisemitism is just something that I condemn completely."
Labour MP Wes Streeting said he had not been in Peterborough to campaign for her since the antisemitism controversy erupted.
He said: “The words ‘zero tolerance’ may have meant little to our leadership, but they do mean something to me. When I promised the Jewish Labour Movement that I would stand in solidarity with them, I really meant it.
“If I had knocked on doors this week I would have been a hypocrite.”
Mr Streeting said Ms Forbes's actions were enough to warrant disciplinary action although none was taken.
He added: “She will need to work hard to persuade the Jewish Labour Movement and the wider community that her apology was meaningful and that she is genuinely committed to tackling antisemitism.”
Labour MP Jess Phillips said the win for Labour showed “that antisemitism is becoming normal in the party.”
She said she would accept Ms Forbes's apology but wanted her to prove that she was committed to making amends.
She added: “With every [antisemitism] case the party’s values chip away and our ability to stand up against hate erodes.”
Dame Margaret Hodge said she had mixed feelings about the win for Ms Forbes because she did not want the Brexit Party to win a seat "but Lisa Forbes and the Labour Party have a lot to answer for. We must learn lessons and never have a repeat of this."
She said she had formally raised concerns with party's leadership.
Ms Forbes was also revealed to have signed a letter last August, to Labour’s governing body, which appeared to call for the dismantling of the state of Israel.
The letter, signed by more than 100 left-wing anti-Zionist campaigners, was circulated by the pro-Corbyn fringe group Jewish Voice For Labour and suggested Israel was not “democratic” but an “apartheid state” and a one-state solution “in the form of a democratic state that grants equal rights to everyone lawfully residing within its borders.”
The letter also opposed the adoption of the full IHRA definition of antisemitism including examples of how criticising Israel could be antisemitic.
The letter was also signed by Elleane Green, who remains suspended by Labour over her running of the Palestine Live Facebook group.
Other signatories included Lesley Anne Perrin, who resigned from Torbay Labour Party over posting Holocaust denial material online, Asa Winstanley, who called the Jewish Labour Movement an "Israeli embassy proxy" and members of the Labour Against The Witch-hunt group.
