Chris Parkin, 47, described "the most surreal five minutes ever" as the star and his girlfriend, actress Dakota Johnson, visited The Stag Inn in Hinton Charterhouse late on Sunday afternoon.
The singer-songwriter hopped onto the piano after a couple at the pub, currently planning their wedding, mentioned their first song will be Coldplay's A Sky Full of Stars.
"He just said, 'Well, do you want me to play it?' It was really brilliant, a brilliant moment," Mr Parkin told the PA news agency.
"It's always a little bit of a shock, things like that.
"It was one of those things where you go, 'Right, this is happening'."
In a video posted to the pub's Twitter account, the star asks the couple their names before playing his band's hit song to the room.
"You never know who might pop in for a pint!" the account wrote.
Mr Parkin described the moment earlier on when Martin walked into his pub alongside Johnson - the daughter of Hollywood stars Melanie Griffith and Don Johnson - whom he did not recognise.
"I said, 'He looks a bit like Chris Martin'," he said.
"And his PA said 'Yes, that is Chris Martin'."
"I had absolutely no idea (who Dakota Johnson was)... The younger girls in the kitchen were like, 'That's Dakota Johnson! She's really famous!'"
Mr Parkin also introduced Martin to his 13-year-old son, Alfred, who is a budding pianist.
"He can play Clocks and can play various songs of theirs and (he is) classically trained on the piano," he said of his son.
"And in fact, (it was) the only reason I stopped him... I said, 'I hate all that camera in your face business. But you wouldn't just say hello to my son?'
"And he just went, 'Yeah, no problem.' He was lovely."
"It was weird, but on the other hand, brilliant - you know?
"It kind of just unfolded, it unfolded like it does and you're thankful when things like that happen, aren't you?"
Mr Parkin said he had been to every Glastonbury since 1995 but having stopped attending over the last few years, did not feel as though he had missed out this time thanks to Martin's visit.
"It felt like Glastonbury visited me," he added.
"I saw their first Glastonbury gig and I've seen every other Glastonbury they've ever done so I've kind of watched them develop as a band.
"Love them or hate them, they are part of British culture, aren't they? That's the thing."