The 28-year-old, currently fourth in the Premier League scoring charts with 17 goals, was embroiled in a number of tussles at the bet365 Stadium on Saturday.
Costa was booked for dissent by referee Anthony Taylor with less than a quarter of the match played, though he kept his cool after being given a word of caution by Gary Cahill and manager Antonio Conte.
Courtois believes that City intentionally made life difficult for his side, but was happy to see Costa keep his cool for the remainder of the contest and play an important part in the eventual 2-1 away win.
"They were very physical and it was hard to find our usual game," he told reporters. "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."
Costa has 17 goals and five assists in 26 league outings this term, but has found the net in just three of his last nine matches overall.