The Kilmarnock striker was struck by a coin during his side’s 1-0 defeat to the league leaders at Rugby Park on Sunday.
Boyd, an ex-Rangers striker, was also targeted with chants of “fat orange b*****d” from the away support.
The 35-year-old took to Instragram to mock Celtic fans as well as condemn them for their behaviour with some spilling onto the park to celebrate Scott Brown’s injury-time winner.
He shared a video of him getting hit by a coin as well as seats damaged by members of the travelling support.
“We’re lead to believe they’re the Greatest Fans in the World,” he wrote on his Instagram account, complete with sleeping and laughing emojis.
“Wrecking seats, flares and invading the park!
“Oh, and in case anyone didn’t know, I’m, just a fat ORANGE (it must just be my favourite colour) b***tard.
“The shouts and abuse I can handles as a bit of banter even tho if others it would be sectarianism.
“Getting hit with a coin, though, is a step too far.
“Don’t worry, I wasn’t injured but if it doesn’t stop someone will end up with a bad injury.
“Thought those days in British (two Union flag emojis) football were over.”
Following the match Celtic boss Brendan Rodgers criticised the fan who threw the coin.
He said: “Any behaviour like that is not acceptable at all, I think we would all reinforce that.”
This season has seen an assistant referee struck with a coin thrown by a Rangers fan at Livingston earlier in the season as well as Alfredo Morelos by a St Mirren supporter and former Hibs boss Neil Lennon by a Hearts fan in October.