The former Scottish Labour leader claimed the message posted in 2017 by Wings Over Scotland blogger Stuart Campbell “considers gay people to be lesser” because they cannot or do not have children.
She told a sheriff she found the suggestion to be factually incorrect and was offended by it.
The politician also insisted she had never called Mr Campbell a “homophobe”, telling the court: “This whole case is about that one tweet.”
Mr Campbell is suing Ms Dugdale, 37, for defamation over a column she wrote in the Daily Record on 7 March 2017, referencing his “homophobic tweets”.
The tweet at the centre of the controversy, made during the Conservative Party conference on 3 March that year, states: “Oliver Mundell is the sort of public speaker that makes you wish his dad had embraced his homosexuality sooner.”
Mr Campbell, 51, from Bath, has denied it was a homophobic reference to Scottish secretary David Mundell being gay and described it as “satirical criticism” of Scottish Conservative MSP Oliver Mundell’s public speaking skills.
Giving evidence on the second day of a civil proof at Edinburgh Sheriff Court, Ms Dugdale said the tweet had been reported “all over” the printed media and that there was “quite a hostile reaction” to it.
“I think a lot of people considered the tweet to be homophobic and to be offensive,” she said.
Roddy Dunlop, representing Ms Dugdale, asked the MSP about her own view of the tweet at the centre of the case.
She replied: “I consider it to be homophobic.”
Ms Dugdale continued: “Because it considers gay people to be lesser because, in the view of the person who tweeted it, they can’t have children or don’t have children. That is factually incorrect.”
She said she was offended by it and added: “Also, the very fact that David Mundell’s sexuality was referenced at all. I don’t understand why it was there.”
Asked about the assertion the statement was a “joke”, Mr Dugdale responded: “I don’t find homophobia funny in any form.”
The Lothian MSP, from Edinburgh, earlier told the court she has a female partner and said: “Increasingly I felt I had a responsibility to call out homophobia, as a gay politician.”
She later told the QC she is entitled to her own view of what she considers homophobia to be, saying she has experienced it in a number of forms.
During cross-questioning, Ms Dugdale told Mr Campbell’s QC, Craig Sandison, she had found the Wings Over Scotland Twitter feed to be “caustic” and “critical”.
She described the pursuer as being in the “top ten” of people who were, in the lawyer’s words, “disobliging” about her.
The court heard Mr Campbell had collated around 120 of his past tweets which show, it is claimed, his positive view of LGBT people.
Mr Sandison asked: “Do you consider him [Mr Campbell] a homophobe?”
Ms Dugdale replied: “No, I’ve never called him a homophobe ... no, I believe what he said in his tweet to be homophobic. I’m stating very clearly I consider his tweet to be homophobic.”
She claimed the tweet was derogatory towards both David and Oliver Mundell. She said: “I honestly believe this is designed to undermine Oliver Mundell on the basis of his father’s sexuality.”
Mr Sandison put it to the MSP: “I suggest your target in that article wasn’t the tweet, it was the man.”
Ms Dugdale replied: “No, I disagree. I was calling out what I consider to be a homophobic tweet.”
On Monday, Mr Campbell told the court: “I don’t believe any intelligent person could honestly interpret that tweet as homophobic, given what it said.”
He said he was “absolutely horrified” to have been accused of homophobia and said the tweet was a “joke”.
Mr Campbell said he has always found discrimination against gay people “abhorrent”.
The case before Sheriff Nigel Ross continues on Wednesday when both sides will make their submissions to the court.