Meanwhile, Mourinho believes playing in front of Cesc Fabregas is a dream for Costa.
Costa, who passed a late fitness test on a hamstring injury, scored a hat-trick as Chelsea beat Swansea 4-2.
The £32m summer signing from Atletico Madrid has seven goals in his first four games for the west London club.
"He is one of the best strikers at this moment in football," Mourinho toldBBC Sport."He is a special player."
Costa cancelled out John Terry's early own-goal with a header on the stroke of half-time and pounced twice after the break from close range to swing the match Chelsea's way.
He departed to a standing ovation from the home fans, who then watched Costa's replacement Loic Remy score his first goal for the club since joining for £10.5m from QPR.
"The team is an attacking team that creates a lot of chances and spaces for a striker," said Mourinho.
"The second goal is a brilliant collective action. (Cesc) Fabregas had a fantastic assist and Diego put the ball in the net. Diego is a good player but he is in a good team."
Costa's goals have added another dimension to a side that finished third in the league last season.
He has already scored two more league goals than Fernando Torres and Demba Ba each managed for Chelsea in the whole of last season, and only two fewer than Samuel Eto'o.
Fabregas, the former Arsenal captain signed from Barcelona, laid on two assists for Costa, who joined in a £32m deal from Atletico Madrid after long being coveted by Mourinho.
"To play with Fabregas is the dream of every striker," Mourinho toldChelsea TV.
"The guy sees the movement, sees the pass, is not selfish, makes always the right choice."
Fabregas added onChelsea 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.