Conte was snappy with reporters and pundits after their 0-0 draw with Shakhtar Donetsk, which left them bottom of their Champions League group and out of Europe.
"Today it was impossible to speak with Conte," Capello said after Conte had left.
“He did not understand that we cannot speak only when things go well. Inter have suffered a huge economic damage this evening, the are not even going to play in the Europa League. The damage is huge, even for sponsors."
"I am very disappointed in my friend Conte," Billy Costacurta continued.
“I am very sorry that he did not respect us. He is a unique and generous person, but tonight I did not like him. I'm very disappointed by his attitude."
Later on, talking about Atalanta, who, instead, have qualified for the last 16 stage for the second successive season, Capello added:
"[Gian Piero] Gasperini is a coach. He is smart. He understood that he had to change something tactically. He understood that he could not play like he did last season. This is the strength of a coach. [Massimiliano] Allegri is another one who changed tactically, who read the game. I'll stop here."