Premier League champions Chelsea agreed to sell Spain worldwide Costa back to Atletico Madrid on Thursday - ending a standoff between the 28-year-old and the club for whom he was top scorer in his three seasons at Stamford Bridge.
"It's not the way I wanted it leave, ever", added Costa, who scored 58 goals in 120 appearances for the Blues, including 20 in the Premier League last season as Chelsea won the title.
Chelsea announced that a deal had been brokered with Atletico Madrid for the sale of the player.
As reported by the club's official website, Morata said: "Alvaro performed very well".
"We want to thank him (Costa) for what he did with this club".
Costa will complete his move in January, when the transfer window reopens and Atletico's ban on signing new players comes to an end. "We wish him all the best for the future", the Italian told reporters.
Pedro scored Chelsea's other goal as Antonio Conte's side maintained its ideal away record in the league, keeping it within three points of United and City at the top of the table.
He is a fantastic player, he scored goals and is someone you would think, 'I'd love him in my team'.
"The one I'd like to play against the most, like's the wrong word, possibly Aguero", Carragher said.
"That's my country, I will return, and I don't know when but that's the aim".
Chelsea face Atletico in a Champions League group stage match in Madrid next week, though it is not yet clear whether Costa will be unveiled before then.
And football fans, particularly Chelsea supporters, are liking what they see. We are managing his recovery very well.