The boisterous duo took the set to discuss the fight Saturday in Las Vegas.
It quickly became heated after Smith sounded as if he was slighting Mayweather's style in winning the bout against the UFC star.
"He was what he had to be," Atlas said on ESPN. "His character. His championship character and his big, big, big advantage of experience and belief in himself in this kind of format allowed him to dominate the guy in a way that he usually doesn't dominate guys. He was able to pull that ace out of the deck when he had to."
Smith disagreed with the legendary trainer-turned-analyst and said that Mayweather "was not great."
The exchange then became very lively.
"What I'm saying is McGregor forced a gourmet chef to be a fast order cook," Atlas said. "That's what he did. He fought a gourmet chef. "
"But doesn't that make him fast food?" Smith asked.
The duo then argued about steaks and fast food before Atlas' response.
"He made him go in there and he made him flip cheeseburgers," Atlas said. "He made him do something that he doesn't normally do."
Then Atlas got super heated.
"But his character still allowed him to walk the guy down and knock the guy out," Atlas said as he stood over Smith with his arms waving.
"What I'm saying to you is this," Smith said. "If you go to a restaurant and get some steak, some fillet minion, and instead you get a burger, ain't it a burger? I mean it's just a burger. That's what we saw tonight."
"It's still a cheeseburger," Smith said. "It's not a steak."
"But who's eating it?" Atlas screamed. "Floyd's eating it. The other guy's not."
Mayweather won the bout in the 10th round after a TKO. Referee Robert Byrd stopped the fight.