Costa led Conte's men to the Premier League title during his first season in charge at Stamford Bridge but was cast aside by the Italian, who made it clear that he was no longer a part of his plans during the summer.
The fiery Spaniard did not take the news well and went public about his unhappiness and desire to return to Atletico Madrid, who have agreed a £53m deal with Chelsea to take him back to the Spanish capital.
The situation involving Costa was an unwanted distraction at the start of Chelsea's season and Conte understandably wants to leave the whole sorry episode in the past, though he was keen to extend his gratitude for Costa's efforts last season.
"I think now it's not important, I'm not interested in talking about this, I'm happy working with my players, it's not important," Conte said in his press conference. "We want to thank him for what he did with the this club and wish him all the best for the future. I'll never forget we won together."
When pressed about Costa, Conte said: "I repeat now I'm not interested in talking about the past. The past is not important, for every coach and player, if you did well in the past it's okay but I think we have to work in the present."
Alvaro Morata is certainly Conte's first-choice forward at Chelsea, but the former Italy boss thinks Costa's departure could pave the way for Michy Batshuayi to truly establish himself in west London after rarely featuring during his debut campaign in England.
"Batshuayi is one of the players in our squad," Conte said. "Last season he didn't play a lot but after one year I think he's worked very hard to be prepared to face this league, he will have the right chance to help us."