The striker was heavily linked with a move back to his former club last summer after enduring a frustrating 2015/16 season as Chelsea failed miserably to defend their Premier League crown.
The two clubs were reportedly in negotiations over the transfer but talks broke down, which meant Costa had to build bridges with Conte.
Costa told El Larguero: “Atletico knows I have a special feeling for the team, I lived the best moment of my career there. El Cholo [Diego Simeone] knows it wasn’t impossible for me to come back to Atletico.
“The relationship with Conte didn’t start well because when he arrived I told him I wanted to go to Atletico. Chelsea’s fans love me a lot, even more than in Atletico, figure that!
“When Atletico had to wait for me they didn’t, there was still a month to go in the transfer market.
“I’ve done everything to come back to Atletico Madrid but I wouldn’t fight the same to return. When Atletico didn’t wait for me, I had to go to Conte with the tail between my legs.”