Courtois developed into one of the best goalkeepers in European football during his three years on loan in Madrid, but returned to parent club Chelsea this summer.
Moya was purchased from Getafe as the Belgian's replacement and has started the season in fine fashion, but the Spaniard has said that he will approach goalkeeping in his own way.
"I don't think people will forget Courtois, because he was a wonderful goalkeeper," Moya told AS.
"I'm Miguel Angel Moya and I try to do my job and help the team."
Moya helped Atletico beat rivals Real Madrid 2-1 in La Liga on Saturday.