Rebecca Long-Bailey said Labour was starting from a “very, very dark place” on the issue, which has caused intense anger among some of the party’s backbenchers.
Last week Dame Margaret Hodge, who lost family members in the Holocaust, confronted Mr Corbyn in Parliament over the party’s failure to take up a strong stance against anti-Semitism.
The row erupted after the party’s ruling national executive committee (NEC) decided not to fully adopt the International Holocaust Remembrance Alliance’s (IHRA) definition.
Ms Long-Bailey insisted the party wanted to “expand” on the examples given in the definition but admitted that the proposals had caused controversy.
“We wanted to develop a code that was legally robust and detailed so that we could enforce it quickly in our disciplinary processes,” she told the BBC’s Andrew Marr Show.
“But we haven’t won the faith of the Jewish community, and indeed my own parliamentary colleagues have expressed concern.
“The intention was never to omit parts of the IHRA definition. The IHRA and examples is a two-sided piece of A4.
“It’s not very detailed but it’s very clear and straight to the point – and what we wanted to do was to build on that.
“We recognise the concerns and that’s why this week it was right for the NEC to look at the code again and look at consulting with the Jewish community to make sure we get it right because we have to restore faith in the Jewish community. We’re starting from a very, very dark place due to the actions of a minority in our party and the failure of us to deal with it quickly.”
She also partly defended Dame Margaret, who is facing an internal party investigation after accusing Mr Corbyn of being an “anti-Semite and a racist”.
Ms Long-Bailey said her colleague had a right to “express her opinion” to the leader of the party.
Shadow chancellor John McDonnell also said Dame Margaret had a “good heart” and that it was right for Labour members to be able to “express anger” when they felt it necessary.
“My view is let’s just resolve this very, very quickly – almost drop the complaint and move on or, if someone wants their complaint investigated, let’s get that done quickly,” he said.