The former Oasis star, whose wife Sara MacDonald is from Edinburgh, also compared the Scottish singer to Star Wars character Chewbacca, telling him to “enjoy his 15 minutes” of fame.
The spat began in an interview with Radio X, when Gallagher told the station he did not know who Capaldi was.
In response, Capaldi played the clip before his Glastonbury show, unzipping a Gallagher-esque jacket to reveal a top adorned with the Oasis guitarist’s face inside a love heart.
He also took a backstage photo with Noel’s brother and former bandmate, Liam, in an apparent jibe to High Flying Birds frontman.
Referencing the stunt in an interview with Variety, Noel Gallagher said: “F****** Chewbacca should enjoy his 15 minutes.
“The greatest day of his life that I slagged him off or called him an idiot.
“It’s the greatest day of his f****** life so far. He’s just thinking ‘wow’.
“Well, I know you’re Scottish and all that but f****** hell. It is like a third world country but for f***’s sake, man, you must have had a better day than this. Surely.”
Not one to shy away from poking fun at himself online, Capaldi reacted to the insults by changing his Twitter name to “Chewis Capaldi”.
He also changed his profile picture to an image of his face edited onto Chewbacca’s head.
Capaldi is riding high in UK charts after his first album Divinely Uninspired To A Hellish Extent became the biggest selling British album of the last five years.
He announced and subsequently sold out his arena tour before the album was even released – the first artist in the world to do so.