England's Stuart Broad was also highly animated in his send-off of batsman Peter Handscomb after he dismissed him leg before wicket during Sunday's second day of the day-night Adelaide Test.
Bayliss said he was not comfortable with the level of sledging between the two sides.
"Probably not and that goes for both sides but it's just the way the game is these days. I'd like to see the microphones turned down," he told reporters.
"I don't think anyone necessarily has to listen to what is being said but it's grown men playing a very competitive sport and sometimes emotions spill over."
Bayliss denied there was a concerted English plan to unsettle master batsman Smith and the Australian team.
"Certainly not. It's just red-blooded young males competing against each other," he said.
"I think most of the time it's fairly light-hearted. A lot more is made of it in the press.
"After the games and after this series the blokes are together having a beer with no hard feelings. It's just the way the game is played."
Smith and Anderson were at each other before the Adelaide Test.
Anderson declared Australia were bullies with Smith retorting that the all-time leading England Test wicket-take was one of the biggest sledgers in the game.
Cricket Australia chief James Sutherland defended the Australian team for their part in the sledging war, saying the practice didn't mean a lack of respect.
"I do feel very strongly about the spirit of cricket and the way the game is played," he told ABC radio on Sunday. "I do feel conscious of playing hard but playing very fair.
"But I am also very conscious, and I know our players are conscious of, wanting Australian cricket fans to be proud of them.
"Certainly I'm very proud of our team and the way they go about it and, in recent times, the way they have found where the line is drawn."
First Published: December 4, 2017, 8:54 AM IST