Chelsea surprisingly fell behind to a Scott Arfield goal at Turf Moor but they came storming back as Costa, Andre Schurrle and Branislav Ivanovic all struck.
Mourinho was impressed with the way his team played and paid tribute to man-of-the-match Fabregas and striker Costa, who were both making their competitive debuts for the club.
He told Sky Sports: “We had control of the game and in some moments we had the quality and style which we want to play.
“You gave Cesc the man of the match and I completely agree. He was the maestro and controlled the tempo of the game with (Nemanja) Matic.
“He dictated the speed and intensity of the game
“Diego did something very important for us which was the first goal. His movement and interaction with Eden (Hazard), Oscar and Schurrle was very good, although I feel sorry for him because it was a penalty and never a yellow card.”
Costa was booked when he appeared to be caught by Burney keeper Tom Heaton, and Mourinho believes there should be a system where yellow cards are reviewed.
He said: “When it is clear that it is not a simulation, I think obviously the yellow card should be taken away from the player.”
Mourinho is confident that Chelsea are on the right path to a successful season, having had little time yet to work with his whole squad after welcoming many of his players back late from the World Cup.
“We have had no more than six or seven sessions with everyone together but we knew the direction we wanted to go,” he explained.
“I always thought that Diego and Cesc would bring us to the dimension we want because they are different players to what we had in the past.
“We need that striker who can hold the ball and have interaction with other players, and we need that kind of midfielder that dictates the intensity in the centre.”