The controversial hitman refused to return to West London after the summer break due to manager Antonio Conte informing him that he was no longer wanted.
In a number of media interviews, the 28-year-old, who accused the Blues of treating him 'like a criminal', made it clear that he only wanted to join his former club Atletico Madrid.
A deal could not be reached in the summer window, but last week the clubs confirmed that an agreement has been made to complete a transfer in January for a reported £53m fee.
Even if Costa had joined Atletico in the summer, he would have been ineligible to play until 2018 due to a transfer embargo imposed on the Spanish club, which prevents them from registering new players.
While speaking about the saga to Marca, Fabregas said: "It's a shame for him more than anyone. Diego knew that by signing for Atletico he could not play for a few months. It has been a difficult situation for him, for Chelsea. It has been wrong.
When asked if he had wanted the striker to stay, the ex-Arsenal star replied: "Clearly. Diego will always [be a friend] and never a rival. In recent years, like a pure No.9, there has been no one better than him.
"I understood him myself perfectly. He knew my football, he read my passes and, most importantly, he got them. He gives a lot to the dressing room. He is not only the Diego that is seen on the field. He is a character that greatly encourages the group."
Costa scored 52 Premier League goals across a three-year spell at Chelsea.