The feisty striker was sent a text by manager Antonio Conte at the end of last season stating he was not in his plans for the upcoming season.
Costa subsequently refused to show up to pre-season training and instead spent the summer in Brazil.
And Fabregas, who plays with Costa for Spain, has expressed his frustration at how his international teammate has been treated.
"It's a shame for him more than anyone," Fabregas told Spanish newspaper Marca.
"Diego knew that if he signed for Atletico he could not play for a few months.
"It has been a difficult situation for both him and for Chelsea; it has been wrong."
Costa has since completed a move to his former club, Atletico Madrid, but he will not be able to play for them until January due to their transfer embargo.