Costa was serenaded with chants and received a standing ovation from the home crowd when he was substituted in the second half of Wolves' 3-0 defeat to Chelsea in the Premier League on Saturday.
Costa previously spent three seasons in the Premier League with Chelsea, scoring 52 goals in 89 top flight appearances.
He won two titles with the Stamford Bridge outfit before a falling out with then-Chelsea boss Conte in 2017 led to his departure to Atletico Madrid.
Costa was born in Brazil but has represented Spain at international level, winning 24 caps for La Roja and scoring ten goals.
"It was special," Costa said of his reception to ESPN.
"Feeling that you did your job when you were here and then leaving with good memories.
"Receiving this affection from the Chelsea fans. I’ve always had affection. I have nothing to complain about the Chelsea fans. When I was here, they always treated me well.
Speaking on his exit from the club, Costa added: "It wasn’t the fans. It was with that coach [Conte]. I had a very good relationship with the Chelsea fans. I was a champion! It was in the year that we won the second title. He didn’t count on me as much and I couldn’t stay.
"The affection I received today shows that I was never fighting with the fans. But I had to leave. It wasn’t my issue.
"It was because of the coach at that moment. Today is proof that the crowd has always been by my side and had affection for me."
