During a timeout, a handful of Clemson fans were shown on the video board with overlaying comments suggesting they were bandwagon fans.
Among the digs: "Thinks That Clemson Is in Georgia," "Can't Name Clemson's Last Head Coach," "Also a Patriots Fan" and "Thinks 'The Fridge' Is Just a Kitchen Appliance."
"The Fridge" was former Clemson All-America defensive lineman William Perry's nickname.
The Greenville (South Carolina) News reported that Cunningham apologized to Tigers athletic director Dan Radakovich and Clemson president James Clements on Sunday.
Robbi Pickeral Evans, UNC's associate AD for strategic communications, told the News that Cunningham has responded to emails from upset fans.
"We want everyone who comes to Chapel Hill to have a positive experience on our campus - whether they are our supporters or our opponents' fans, first-time visitors or long-time guests," Cunningham wrote. "The video board spot featuring Clemson fans on Saturday was not in that spirit.
"We regret that it was produced. ... We addressed the inappropriateness of the spot with the responsible staff members immediately after it was shown, and we will continue to address this week the breakdown in process that led to it."
The defending champion Tigers won their 20th consecutive game only after they stopped the Tar Heels' two-point conversion try with 1:14 to go.
Clemson survives big scare from North Carolina
The Clemson Tigers go into Chapel Hill and barely escape with a win, taking down the Tar Heels 21-20.