The former Arsenal skipper recently claimed that Wenger, who won two Premier League and FA Cup doubles with Adams as his captain, "couldn't coach his way out of a paper bag".
Adams suggested that Wenger did not want him back at the club in a coaching capacity due to a potential challenge to his authority, but the Frenchman insists that former players have no divine right to expect a job after they retire.
Asked if he had been hurt by Adams's jibe, Wenger told reporters: "No. He can show what he can do now. Who gives importance to that? I know him for a long time. It's sad. I am respectful to everybody. I don't have anything to say about that. For me it's a subject of no interest. And so I would like to dedicate my time to something that is more interesting.
"Look, in a football club today, you have to employ people who can help you to be successful. Sometimes it is to make harsh decisions. You have to be needed. And like you have made a career as a player somewhere, it doesn't give you any divine right to come back. That's what it is.
"Because all the players, at some stage, they decide to leave, when their interest was to leave. It is not like some players have never left the club. When it was their interest to go somewhere else, they went somewhere else."
Adams is currently in charge of La Liga side Granada, where he has lost all seven of his matches.