Richards believed Conte was “being absolutely honest” and did not say “anything wrong”, while Sutton took the opposite view.
“Sometimes you need those home truths,” said former Manchester City defender Richards.
“Tottenham have had enough quality to do better than they have been, so I have no problem with that interview from a player’s point of view.
“Of course, it’s not going to be good for the morale, but it’s honest. The players, for their ability, have not been playing well enough.
“It’s an interview where he’s been honest. It’s not terrible leadership. He’s at the end of saying what he’s had to say to the players, so he’s saying it out loud.”
Former Blackburn striker Sutton said the Italian’s outburst “was purely about self-preservation and Conte isn’t bothered about who he takes down”.
“Conte’s been there for however long and the club have gone backwards,” he added. “The most remarkable thing about the interview was that he absolved himself of any blame and things he could affect. He could’ve affected things at the weekend against Southampton and didn’t.
“This is a guy that clearly wants out. It’s terrible leadership. Players within that dressing room will be thinking the manager doesn’t have our back.
“It’s a really important end to the season for Tottenham and there may be a lot of players within that dressing room who down tools for him now. Why would you want to play for this guy now?”
Richards, however, also cited Conte having to deal with, external the death of friends Gian Piero Ventrone, who was the Spurs fitness coach, Gianluca Vialli and Sinisa Mihajlovic, as well as having gallbladder surgery in February.
He added: “If you look at the whole thing, what he’s had to deal with in terms of injuries, the whole Harry Kane situation about whether he is going to sign a new contract or move on, your best midfielder [Rodrigo Bentancur] getting injured, Dejan Kulusevski getting injured, then the people passing around you who are good friends.
“It is going to have an effect on what you are going to say in a press conference. At the end of the day, he is a human being,” said Richards.
“That news conference for me was all his emotions coming out after that game. Maybe he is at the end of his tether.
“I understand his frustration of him being a great manager and not being able to deliver what he wants to do at Spurs. I think it’s a mix of everything.”