Mr Corbyn drew criticism for his response to a Facebook post by street artist Mear One about a plan to paint over the controversial east London mural.
The former Shadow Business Secretary told BBC Newsnight: “There clearly is an issue around anti-semitism in the Labour Party. It isn’t that the majority of our members are anti-semitic but there is definitely amongst the minority a real problem here that is not in keeping with the Labour Party.
“The way the party has dealt with this issue over the last couple of years has been shameful.
“If we were dealing with a situation where we had these examples of hatred and discrimination emanating in and around the Labour Party, say with regard to black people, I would not stand for that kind of thing and I would be very surprised if the Labour Party dealt with instances of racism like that in the same way.
Chuka Umunna slammed the Labour Party for allowing anti semitism to fester
“It is a crying shame and it is something that frankly is unacceptable the way we have been dealing with anti-semitism. We must get our house in order.
“There clearly is an issue here, our values and our principles demand that we deal with it and we haven’t been doing so properly to date.”
Mr Corbyn’s response to Mear One questioned why the painting was being destroyed and said the artist was “in good company” because the Rockefeller family had covered over a work featuring Lenin in their New York development.
The mural, in east London, depicted a group of businessmen playing a Monopoly-style game on a board balanced on the backs of people.
The artist denied being anti-Semitic, saying the mural is about “class and privilege” and contains a group of bankers “made up of Jewish and white Anglos”.
Sajid Javid, the Secretary of State for Housing, Communities and Local Government, called on Corbyn to answer questions in Parliament on anti-semitism.
He tweeted: “Enough is enough Jeremy Corbyn. I’m going to ask for a debate in Parliament on anti-semitism in coming weeks.
“I challenge you to turn up and personally speak for the Opposition. Your opportunity to explain why you defend the world’s oldest hatred.”
Mr Corbyn said he made a “general comment about the removal of public art on grounds of freedom of speech” but acknowledged he should have looked more closely at the image before posting on Facebook.
He said: “I sincerely regret that I did not look more closely at the image I was commenting on, the contents of which are deeply disturbing and anti-Semitic.”
Prominent Labour backbencher Yvette Cooper has said she is “really troubled” by Jeremy Corbyn’s office’s handling of a row over an allegedly antisemitic mural.
The chairwoman of the powerful Commons Home Affairs Select Committee said she “strongly agreed” with Labour and co-operative MP Luciana Berger, head of Jewish Labour, who said the response by the leader’s office was “wholly inadequate” and failed to understand “on any level the hurt and anguish felt about Antisemitism”.
Chuka was speaking live on BBC Newsnight
Ms Cooper tweeted: “Strongly agree with Luciana Berger – am really troubled by the mural, the comments and the way this was handled today.”
Labour MP Wes Streeting compared the failure to act on anti semitism within the party to the dismissal of Owen Smith as Shadow Northern Ireland Secretary.
A member of the Treasury Committee, he tweeted: “If only antisemites were dealt with as swiftly and severely as Remainers.”
Pro-European Labour former Northern Ireland Secretary Lord Peter Hain called Mr Corbyn’s decision to sack Mr Smith “a terrible Stalinist purge”.
Mark Urban was the presenter for the Friday night programme
He wrote on Twitter: “This is a terrible Stalinist purge.
“Owen Smith has been doing a terrific job on Northern Ireland he’s ideal for the role with his experience expertise and considerable ability. Widely respected.
“In a Shadow Cabinet with few big hitters, he was definitely one.”