Sarah Champion faced a backlash after writing in the Sun that "Britain has a problem with British Pakistani men raping and exploiting white girls".
The Rotherham MP quit as shadow equalities minister and apologised for her "extremely poor choice of words".
The Labour leader denied claims he had sacked Ms Champion for speaking out.
He told BBC Manchester: "Child exploitation is wrong. Child abuse is wrong. It is a crime, and it has to be dealt with.
"But you cannot blame an entire community, an entire nation or an entire ethnic community. You have to deal with it for the crime of what it is."
Asked if he had sacked Ms Champion over her comments, he said: "Look, she resigned and I accepted the resignation, so, clearly, I think it's right thing to do and I thank her for her work."
Communities Secretary Sajid Javid accused Mr Corbyn of stifling debate.
The Conservative minister said in a tweet: "Corbyn wrong to sack Sarah Champion. We need an honest open debate on child sexual exploitation, including racial motivation."
Business Minister Margot James said she was "enraged" by the Labour leader's "treatment of Sarah Champion".
She wrote on her Facebook page that the Rotherham MP's comments "might have been hard hitting, but that doesn't make them any less true".
The Conservative MP for Stourbridge added: "There needs to be a discussion about how we overcome the cultural attitudes towards women that have contributed to these crimes; and to the ways in which they were covered up for so long.
"There has been a disgraceful history of shouting down brave Labour women MPs who have stood up to community pressures in Northern cities like Keighley (just google former MP Ann Cryer) and Rotherham in exposing these crimes, of which the appalling treatment of Sarah Champion is yet another chapter."
Conservative former Children's Minister Tim Loughton said he did not know if Ms Champion had been sacked or not - but he accused Mr Corbyn of being "deaf to a problem that is happening in our country".
The Equality and Human Rights Commission said it was a "real shame" that Ms Champion had resigned because of "over-sensitivity about language".
Labour's shadow justice minister, Yasmin Qureshi, refused to be drawn on whether it was right that Ms Champion had stepped down.
"I think you need to ask Sarah that question," she told BBC Radio 4's Today programme.
"Of course we should deal with abuse wherever it occurs and we should ask ourselves as to what we can do to ensure these things don't happen."
Ms Champion's article was written after 17 men were convicted of forcing girls in Newcastle to have sex.
The men, who were mostly British-born, were of Iraqi, Bangladeshi, Pakistani, Indian, Iranian and Turkish heritage.
In interviews following the convictions, the Labour MP said such crimes involved "predominately Pakistani men" and a fear of being called racist was hampering the authorities' investigations.
She then wrote the Sun article, which also included the line: "These people are predators, and the common denominator is their ethnic heritage."
Among the article's critics was fellow Labour MP Naz Shah, who said it was "irresponsible" and "setting a dangerous precedent".
Following the backlash, Ms Champion sought to distance herself from the article, claiming it had been altered, something denied by the newspaper.
Announcing she was stepping down, Ms Champion said: "I apologise for the offence caused by the extremely poor choice of words in the Sun article on Friday.
"I am concerned that my continued position in the shadow cabinet would distract from the crucial issues around child protection which I have campaigned on my entire political career.
"It is therefore with regret that I tender my resignation as shadow secretary of state for women and equalities."
Jeremy Corbyn has said it is wrong to blame "an entire ethnic community" for child abuse after one of his frontbench team quit over a press article.