The rock legend added that he was a "traditionalist in that sense", before comparing Swift to Billie Eilish and her brother, Finneas.
"I'm more attracted to that than to Taylor Swift. It's just darker – less endlessly upbeat. Way more minor and odd. I think (Billie's) exceptional."
Within hours of it being posted, Swift retweeted a link to the article, along with a scathing message aimed directly at Albarn.
"I was such a big fan of yours until I saw this. I write ALL of my own songs. Your hot take is completely false and SO damaging," the All Too Well singer wrote.
"You don't have to like my songs but it's really f***ed up to try and discredit my writing. WOW."
She followed it up with: "PS I wrote this tweet all by myself in case you were wondering."
Within an hour, Swift's furious response had attracted more than 150,000 "likes" and 30,000 retweets.
New Zealand producer and songwriter Joel Little, who worked with Swift on her album Lover, rubbished the musician's claims she didn't write her own songs.
"Just to confirm what 99% of people already knew, @taylorswift13 is a force of nature in the studio and one of the best to ever do it," he wrote.
"Anyone who's made music with her knows they were lucky to be in the room."
Record producer and songwriter Jack Antonoff, who has worked with Swift for seven years, jumped to Swift's defence just minutes after she tweeted.
"If you were there ... cool ... go off. if not ... maybe ... shut the f*** up?" the 37-year-old Lorde collaborator fired on his Twitter account.
"I've never met damon albarn and he's never been to my studio but apparently he knows more than the rest of us about all those songs taylor writes and brings in."
After receiving backlash on social media, Albarn left a public apology under Swift's tweet: "I totally agree with you. i had a conversation about songwriting and sadly it was reduced to clickbait.
"I apologise unreservedly and unconditionally. The last thing I would want to do is discredit your songwriting. I hope you understand."
It wasn't just Swift in Albarn's firing line – the Blur frontman also took a shot at his own work, specifically the song that made him so famous: Song 2.
"That's a perfect example of something that's more about attitude and production than actual cracking songwriting," he told the interviewer