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 £32 million signing from Atletico Madrid.
"The only think 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."
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."
2014-15 Premier League, Chelsea, Diego Costa (AFP)
Erm, apologies Jose, but the only disappointing moment from the incident was Costa’s needless provocation of Coleman following the Everton defender’s unfortunate own goal.
It’s a shame Mourinho feels the need to highlight the treatment of Costa by opposition players and referees, given his actual performances have been excellent. The striker’s chance-conversion rate is very impressive and while there was an element of luck surrounding his opener against Everton, there was nothing dubious about his second.
Mourinho was rightly disappointed by his side’s defending, but he’ll be delighted at how they repeatedly exposed a very sound Toffees backline – especially given their woes in front of goal at certain stages last season.
WHAT HAPPENS NEXT?
Costa keeps scoring, probably. Chelsea have two home games against Swansea and Schalke after the international break before heading to the Etihad Stadium for the first proper test of their title credentials.
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- Seamus Coleman