Manager Jose Mourinho said he had built his side to accommodate the powerful Brazil-born Spanish striker but he also tried to calm expectations and take the pressure off his new recruit.
"If the team plays well he has to score goals," Mourinho told reporters after a 4-2 win opened a two-point gap for Chelsea at the top of the Premier League.
"But seven goals in four matches is maybe too much. You can not expect that he will score eight in 14 games.
"It's not normal," added Mourinho in answer to a crowd that chanted 'he scores when he wants' after Costa, returning from a hamstring injury picked up on international duty, completed his treble in the 67th minute before giving way to fellow new signing Loic Remy.
The manager said that since he arrived for his second spell at Chelsea last season he had constructed a side that would need a "certain type of striker".
Out went expensive flop Fernando Torres, Demba Ba and stop-gap Samuel Eto'o and in came Costa and France frontman Remy who scored Chelsea's fourth on his debut against Swansea.
"We did well waiting and waiting for the right man," Mourinho said of Costa.
Chelsea looked lacklustre in the opening half hour, their midfielders failing to find Costa and suffering against a disciplined, speedy and confident onslaught from Swansea who started the game as the only other unbeaten side in the league.
PANICKED TERRY
Swansea went ahead in the 11th minute when a panicked John Terry attempted to clear a Neil Taylor cross and managed only to push the ball into his own net.
"They had too much time, too much space," Mourinho said. "The second half was fantastic for us. We made changes and were too strong for them."
Mourinho took off the underperforming German Andre Schuerrle and added the indefatigable Brazilian Ramires at halftime, Chelsea upped the intensity and Swansea could not stay with them.
Costa had equalised just before the break with a pinpoint header from a Fabregas corner, bursting Swansea's bubble.
Mourinho was anxious to play down Costa's exploits, saying: "You want to speak about names and players and I want to talk about the team and collective.
"Maybe there were players you didn't see that were fantastic, for example Ramires."
Such was Costa's impact the crowd barely noticed their hero Didier Drogba did not even make the bench.
Drogba began a second spell at the club in the close season and Mourinho dismissed comparisons between Costa and the 36-year-old Ivorian who spent eight campaigns at Stamford Bridge before leaving in 2012.
"Didier had a fantastic career at Chelsea but we can't compare the players and the teams. Diego plays in a different team with a different style," he said.
(Editing by Tony Jimenez)
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