"The most important thing of a player's character is what affects his performance as a player," Mourinho said. "Diego was a risk and a doubt before Everton, a risk and a doubt before Spain, a risk and a doubt before this Swansea game and he played all three games. He is a risk and a doubt again for next Wednesday because of an accumulation of matches, but nobody can stop him.
"I tried to rest him, I tried to be sure. To be 100 per cent sure, but he goes on. He is a fantastic character. If the injury is a clear injury of course he will not play, but when the doubt is there and he has not the best feelings, but he feels he can play, he goes on."
Mourinho agreed that Costa's ability to play through pain is similar to his captain, John Terry's. When asked if that mentality is unusual among modern footballers, he said: "It is not about the modern player, it is about the modern society. The education they get, the people they have sometimes behind them to make them be a little bit more selfish in the sense of you first and the team second.
"This concept of the team first and me second. The team needs me and I am ready to go for the team. I am not saying it is an old-fashioned concept, no way, but in this moment when you get guys with this mentality they become special and they can be an influence to the people around them. He is a leader of himself. He knows exactly what the team needs and is ready to give to the team. It is important to be strong."
Costa is certainly strong. He has bullied defences in Spain and now England, but insists he is more than just a fighter. "I play in the fashion that I have to play," Costa said. "If I have to have a physical battle, then I can fight. If I have to play with quality, I can do that too."
Costa became the second player to score in his first four Premier League games, equalling Micky Quinn's achievement for Coventry City in 1992. "I am very happy to have this record," Costa said. "A striker has to score and I am happy that I have a little place in history. I have to keep working to make sure I can keep this up."
Despite settling in so quickly on the pitch, the Brazil-born Spain international admits he is yet to adapt to life in London, but is delighted with the support he is receiving from his teammates.
"I have not been out in London, but I am trying to get to know it and bit by bit adapt to London. It is clear that it is a new country and a new team and to have old team-mates [Filipe Luis] is very important. Ramires, Willian, Oscar, Cesc Fabregas and Cesar Azpilicueta have all helped me a lot as I try to settle in and the people inside the club, too. They have treated me very well. I am very happy."
Addressing the fact that he has adjusted to his new club better than Fernando Torres did, Costa said: "It is different for every striker. Every striker has their way of playing."
Costa's goals helped Chelsea to maintain their 100 per cent start to the season and ended Swansea's run of successive victories.
