Costa struck a hat-trick - taking his tally to seven goals from four Premier League games - as Chelsea beat Swansea 4-2 on Saturday to extend their 100 per cent winning start to the season.
Midfielder Fabregas, the former Arsenal captain signed from Barcelona, laid on two assists for Costa, who joined in a £32million deal from Atletico Madrid after long being coveted by Mourinho.
"To play with Fabregas is the dream of every striker," Mourinho told Chelsea TV.
"The guy sees the movement, sees the pass, is not selfish, makes always the right choice."
Fabregas added on Chelsea TV: "Just trying to do my job
That's it.
"We have a good team, strong, young, with a lot of courage
We showed it again."
Chelsea will have to show more in Wednesday's Champions League Group G opener with Schalke, a match which comes ahead of a trip to Premier League holders Manchester City.
The Blues have scored 15 goals in four Premier League games but, unusually for a Mourinho team, they have conceded five times in the last two games following the 6-3 win at Everton.
"I don't like (conceding), but we were analysing the goals against Everton and trying to identify the mistakes and we'll do the same thing with these two goals (against Swansea)," Mourinho added.
"If you score more goals than the opponent you win, but you want to be more consistent behind because it's not possible to always score four, five, six or three.
"There will come a time when we need a point and a 0-0 is a point or we need a victory and 1-0 is also a victory."
Mourinho will demands his defence improve, but in Costa it seems Chelsea have an added cutting edge this season.
Mourinho has spoken of his upgraded strikeforce following the departures of Fernando Torres (on a two-year loan to AC Milan), Samuel Eto'o and Demba Ba, with Costa, the returning hero Didier Drogba and Loic Remy coming in.
Remy took just nine minutes to open his Blues account after coming off the substitutes' bench in place of Costa.
"For me it was amazing," the striker signed from QPR said on Chelsea TV.
"I'm a striker and a striker wants to score
I was very happy after the goal and after the result.
"Diego Costa is on fire at the minute and that's good for the team
It's good for the team to have his quality.
"I really hope we're going to stay at the same level
Even if I'm on the bench I try to do my best and score goals."
Drogba is a doubt for the Schalke clash with an ankle injury.
Swansea goalkeeper Lukasz Fabianski was beaten by Costa and Remy, but reflected positively on City's performance.
"We'll have to look at both the positives and negatives and draw some smart conclusions from there, but we did well," Fabianski said on swanseacity.net.
"In the first half I thought we dominated the game
We created lots of chances and probably shocked them with how well we were playing.
"But we were hanging on a little in the closing stages of the first half as they had more possession and crosses in the box.
"It isn't a good time to concede and in the second half Chelsea pushed a lot harder."
Right-back Angel Rangel added: "We have to improve on certain areas and that's what we will be working hard on in time for next week's game against Southampton."
Source : PA
Source: PA