Appearing on the BBC's Andrew Marr Show this morning Mr McCluskey, whose union backed Ms Long-Bailey in Labour's leadership contest yesterday, was told of comments by Sheffield City Council leader Ms Dore who said she does not want a "continuity Corbyn candidate".
But he said: "When Julie says she doesn't want a continuity Corbyn candidate, she didn't want Corbyn as a candidate and there's lots of these leaders who are anti-Corbyn so of course they'll try to stick Rebecca with the same tags and that's deeply unfair of them."
Ms Dore, who is retiring in May, told the Guardian previously: “I do not want a continuity Corbyn candidate. It was the most disastrous result ever and we can’t just change the face, change the name, change the gender maybe, and just continue and do what we’ve done before.”
Mr McCluskey described Ms Long-Bailey as "completely different" from Mr Corbyn.
When told she agrees with all of Mr Corbyn's policies, Mr McCluskey replied: "I don't know she agrees with all his policies, I think she agrees with the radical nature of the alternative that Labour offers the electorate but she'll have her different views about what her priorities are."
Mr McCluskey said Labour "never handled the anti-Semitism issue correctly" but said some opponents of Mr Corbyn used it to undermine him as leader.
He said: "I'm absolutely convinced that there were those individuals who opposed Jeremy Corbyn's election right from the beginning, used the anti-Semitism issue - which I think is quite despicable that they did this on such an important subject - to undermine Corbyn, there's no doubt about that."