The 29-year-old played a key role as Chelsea won the Premier League title in Conte's first season at the club but was subsequently told to find a new club over the summer by the Italian.
Costa was presented to Atletico fans on Sunday at the Wanda Metropolitano.
Conte was asked for a reaction and stated: "It's not right to talk about players who are not in my team and squad.
"We won together, so I will always remember him in a positive way. We fought together and won together."