The Spain international scored in the first and last minutes but in between was booked for an altercation with Seamus Coleman, having previously upset his opponents by apparently goading the Republic of Ireland international for his own goal to make it 3-1 in the second half.
Mourinho said he was disappointed with some of Everton's attempts to aggravate his £32million signing from Atletico Madrid.
"The only thing I didn't like in this game - apart from some of our defensive mistakes - was the way some Everton players were trying to create problems for him," said the Portuguese.
"I don't think this is English football
There is a good tradition with Everton teams because everything is good, everything is positive: the manager, the quality of their football.
"But to be chasing cards to a player who once more had good behaviour and was just here to play football is disappointing.
"At the end of the story Diego is maybe the best player in the Premier League in the first three matches and he has two yellow cards; one against Burnley where he didn't simulate - it was a penalty and today when everyone was chasing him to get him in trouble
That is disappointing."
Everton manager Roberto Martinez's response was to suggest Costa's behaviour showed he had yet to learn the standards associated with English football but refused to be drawn into a slanging match.
"I am disappointed if a manager who has won a game away from home complains about the attitude of players," said the Spaniard, who said his side showed fear when the ball came anywhere near their penalty area.
"There are certain foreign players who come to the Premier League who need to understand the ethics and the culture as the behaviour in the British game is unique.
"The last thing you want to see is disrespect from a player to another player and I am sure he will learn that very quickly.
"There is a real professionalism and respect in the league so you can understand why the players weren't happy with that, in the same way of trying to buy free-kicks with the way he plays.
"I will not fall in to that trap of being disrespectful."
Mourinho described Costa's performance as "fantastic in every aspect".
"In the first half he was tackling Coleman on the edge of our box, he recovered balls, he held the ball up, went face to face with Howard two times and scored two goals - his movement, his quality was really good.
"But we made defensive mistakes
It is difficult to believe Wednesday afternoon we trained one and half hours and did only two things: defensive corners and defensive free-kicks.
"So imagine how happy I am with the result of our work
It was better Wednesday to give them free time, stay at home with my wife and kids rather than train when they come here and concede the second goal, which is ridiculous."
Branislav Ivanovic made it 2-0 inside three minutes after Costa's opener and after Kevin Mirallas pulled one back on half-time Coleman's own goal restored Chelsea's cushion at the start of a mad 11-minute spell which also brought further goals for Steven Naismith, Nemanja Matic, Samuel Eto'o on debut, Ramires, and finally Costa.
Source : PA
Source: PA