The Spain striker was wanted back at the Vicente Calderon after a difficult 2015/16 season.
Earlier this week, Costa admitted he was desperate to secure a La Liga return.
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But a deal failed to materialise with Antonio Conte making clear his main striker would not be leaving Stamford Bridge.
And Conte’s power play has seen Costa score 17 times in the Premier League this term.
Chelsea striker Diego Costa
Nevertheless, Atletico boss Simeone insists he is happy with his striker signing Kevin Gameiro’s 14 goals this season and praised Costa as the key to Chelsea’s Premier League title charge.
He told Spanish newspaper AS: ”It could have been something better, or worse.
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Diego Costa has a good relationship with Diego Simeone
"He's doing great at Chelsea and he's probably a key to what's happening to the team.
"Atletico tried everything [to sign Costa], but in England there is no cancellation clause. Diego did his best to come.
"We were always transparent with [Gameiro] in relation to Costa. He knows he was the first choice if Costa did not arrive."