The Spain striker has exiled himself from Stamford Bridge and is currently in his native Brazil trying to force through a move to Atletico Madrid.
Costa believes that it was "disrespectful" of the Chelsea head coach to break the news to him in such a manner.
"Conte's text? It was a moment of madness. It can happen, but I thought it was disrespectful," he told Brazilian outlet MC News.
"I always asked to speak face to face with the coach and the board. I never sent [them] text messages, so it shows what kind of person he is.
"If something makes me sad about this situation, it's [the fans'] affection as they'd always supported me, even during the delicate moments.
"If I'd been in the team for three years, it was for them and the dressing room, which was very much united. It was a great experience."
During his three-year spell at Stamford Bridge, Costa has netted 58 goals in 120 appearances in all competitions.