The Spaniard finally secured his dream move back to Atletico Madrid on Thursday after spending the summer in exile.
Costa refused to return to Chelsea after last season, after claiming Conte had made him 'feel like a criminal'.
The Blues boss reportedly told the forward he had no future at Stamford Bridge via text message.
But speaking in a Brazilian airport, Costa admitted he had no ill feelings towards his former manager.
"I'm not upset with anybody," Costa told Splash News in Sao Paulo.
"I have no bitterness towards anyone.
"Everything is cool."
The 28-year-old was then asked whether he had a message for the Chelsea support.
"Everybody knows how much I love the fans," he responded.
Costa scored 20 goals in 35 appearances last season as Chelsea cruised to the Premier League title.
He will now return to Atletico, where he spent four years earlier in his career.
Costa has not played for 98 days since appearing for Spain against Macedonia in a World Cup Qualifier.
He will train in Madrid but will not be able to feature for his new club until Atletico's transfer embargo is lifted and the transfer window re-opens in January.
Costa is set to watch Atletico's match against Sevilla tomorrow from the stands.
