Conte has mocked Capello's time in charge of Juve in reaction to critical comments from the Russia coach.
"Conte needs to show more respect for the club," Moggi told Sports Mediaset. "He should be asking permission from the club before making those kinds of comments.
"With me in charge this would never have happened.
"Juve under Capello had some important results. This whole issue seems absurd to me.
"To me he is paying Conte a compliment, not a criticism.
"Conte needs to stop making these kinds of quotes. He should show more respect to the club.
"He works in a stadium where it says that Juve have won 31 Scudettos. Now he should say, 'I don't work here.'"