Costa was booked for dissent by referee Anthony Taylor after just 17 minutes at the Bet365 Stadium as Stoke looked to exploit the Spanish striker’s notoriously short fuse.
Chelsea’s stand-in captain Gary Cahill revealed after the match that he had felt compelled to intervene with Costa before half-time in a bid to ensure the visitors kept all 11 men on the pitch.
And Courtois believes it is to Costa’s credit that he kept his cool as Stoke players were trying to pressurise him into losing his head.
"They were very physical and it was hard to find our usual game," Courtois said. "They tried to put our players out of the game by doing that. They know Diego doesn't like it and he maybe starts to fight with people. Maybe they do this to get him a red card or something.
"In some moments maybe Diego exaggerates a bit as well, but I think most of the time they were hitting him quite well. After four or five 50-50 moments where the referee can whistle or not whistle, he gets a bit angry and gets a yellow card. So it's important for him to stay calm and he's developed that a lot this season.
"When they kicked him, he remained calm and that's very good for us because in the worst case, he would have got a second yellow card and been out of the game. It's a good job he remained calm and dealt with what happened to him and moved on.
"Diego is the type of guy who has a lot of energy and goes for every ball and he gets kicked as well. People know how he is as well and a lot of Stoke players got a yellow card for fouls on him. He was always calm and he does well for us."
Despite yellow cards in his last two games Costa’s disciplinary record seems to have notably improved under Antonio Conte. After receiving five booking in his first 10 games of the season for club and country he has received just three cards in the subsequent 24 matches.