The West Lothian singer was due to perform on the Other Stage on Saturday and while fans were waiting for him to appear, Gallagher's comments were played on the big screen.
The rocker bemoaned the state of chart music and singled out the Scottish newcomer, asking: "Who's this Capaldi fella?"
Capaldi, 22, whose album Divinely Uninspired To A Hellish Extent topped the charts earlier this year, then walked on stage wearing a bucket hat, round sunglasses and an Oasis-style green coat.
He threw off the coat to reveal a white T-shirt embellished with Gallagher's face inside a red love heart.
He tweeted earlier in the month: "Lewis Capaldi you big daftie. You might wanna try and find some joy in your tunes you're destroying the youth..my 11yr old is in bits."
Capaldi opened his set with Grace, before treating fans to renditions of Bruises and Someone Like You.
At one point, the charismatic Scot spotted a sign in the audience referring to him as the "Scottish Beyonce".
He said: "Cos that's what I am. Let it be known, spew it from the hilltops. This is the Scottish Beyonce."
Noel's brother and former Oasis bandmate, Liam Gallagher, will perform on the Pyramid Stage on Saturday evening.