During his spell at Chelsea, Conte had run-ins with Costa and told the striker via text message that he was not wanted at the club.
Costa, 31, says he no longer has a problem with Conte and admits he is a talented coach, even if he lacks the "human" touch needed to succeed at a team like Real.
"[Conte and I] had problems off the pitch, but I think he is a really good manager," Costa said to ESPN.
"I have no hard feelings towards Conte, but to be a top, top manager, he needs to change the human side of his management. He is very suspicious. At a team like, say, Real Madrid, he would never last a season."
Although he was born in Brazil, Costa made just two appearances for the national team before switching his allegiance to Spain.
The striker faced criticism for his decision, but he says former Brazil boss Luiz Felipe Scolari made it an easy one.
"After the friendly against Russia, he said he would call me up again because I hadn't played many minutes," he added. "I think it was just to get in my head.
"I remember several forwards were injured but Scolari would not select me. I stayed quiet, but wasn't selected for the Confederations Cup.
"The possibility of Spain emerged and I accepted. How could I say no?
"Suddenly, they started saying Scolari wanted me. Well, he never called me once. How could it be that he wanted me?
"I then saw it written that I had ruined the dreams of millions of Brazilians. Why not say that he didn't look for me? Then it's simple."