She also commented under a post whose author claimed that Islamic extremists were the creation of the CIA and Mossad, the Israeli intelligence agency.
Ms Forbes subsequently apologised for “not calling out these posts” and promised to challenge anti-Semitism in future.
The Jewish Labour Movement had called for her to have the whip suspended and some of her new Commons colleagues were critical of her.
But Mr Corbyn said: “She has apologised for the remarks that she transmitted through social media.
“If there are complaints about her they will be investigated, not by me, but by our party system.”
He added: “She has made her position very clear.
“Lisa Forbes is a good woman. Not a racist in any way whatsoever.”
A Labour source said: “Lisa Forbes did not make any comments herself or share any posts.
“She liked a video about showing solidarity with Christchurch victims without reading the accompanying text, which Facebook users know is an easy thing to do. She has fully accounted for this genuine mistake and apologised.”
Ms Forbes has also said she “fully agrees” with Labour’s position on adopting all the International Holocaust Remembrance Alliance examples of anti-Semitic behaviour.
Mr Corbyn was speaking in Birmingham, where he had been launching Labour’s plans for a new social justice commission to prevent the talent of people from disadvantaged backgrounds being “squandered”.
The Labour leader said he would tackle a system where cash-strapped schools faced having to organise sponsored walks for pupils “to raise money for basic equipment”.
Mr Corbyn said the “social mobility” agenda has failed, suggesting it was only aimed at allowing the “lucky few” to escape disadvantaged backgrounds.
Setting out his plan he said: “The approach is social justice for all rather than the ability of a very small number to achieve a higher position in society.
“What I’m concerned about is, a child born today, you could look at their lives, draw a map of where they live, what the income level of their parents is, and you can make a pretty clear prediction of where they are likely to end up.
“I don’t want that. I want a real chance for every child.”
Education Secretary Damian Hinds said: “Social mobility is not about the lucky few, it is about breaking the cycle of disadvantage and making sure that everyone has the opportunity to fulfil their potential.
“Our education system is doing exactly that with the gap between disadvantaged children and those from a privileged background having narrowed at every stage: pre-school, primary, at GCSE and with more disadvantaged young people going to university than ever before.”