"When I look at Greg and how he's handled himself, on the field and in the locker room, I see a guy that is not aware," Marshall said during a discussion on Showtime's "Inside The NFL" that was broadcast Tuesday night. "He doesn't understand the magnitude of what happened last year, what he did and the atmosphere surrounding the NFL.
"I don't think that he gets it. I don't think that he learned his lesson. And he really needs to look himself in the mirror and ask himself, 'What type of person do I want to be?'"
Hardy missed the first four games of this season while suspended under the NFL's personal conduct policy. He was convicted last year of assault on a female and communicating threats in a case involving a former girlfriend. But he appealed the conviction, and the charges were dismissed in February after prosecutors said the accuser in the case couldn't be found.
After signing with Dallas, Hardy was suspended for 10 games by the NFL for conduct detrimental to the league, a penalty that was later reduced to four games.
Marshall doesn't dispute Hardy's reputation as "one of the hardest-working guys on the field." However, Marshall said he feels the big picture is largely being ignored by Cowboys owner/general manager Jerry Jones.
"Right now Jerry's only focusing on the player," Marshall said. "It's time for us to start talking about the person. It's time for us to start dealing with the person. If we want the product on the field to be great, if we want to protect the shield, then we have to approach both the same."
Hardy also was involved in a sideline incident during Sunday's loss to the Giants in which he swiped at special-teams coach Rich Bisaccia's clipboard, which led to Bisaccia shoving him out of the huddle. Words continued as Hardy got into it with Devin Street. On the sideline, he exchanged words with Dez Bryant, who was attempting to calm things down.
It's at least the third time this season that Cowboys coach Jason Garrett has had to talk to Hardy about his actions.
"There's emotions that come with the game," Marshall told Showtime. "There's a lot of testosterone. I mean, you put so much into the week, you know? You get disappointed, and you get frustrated in those moments."
Jones, meanwhile, has lauded Hardy for being "one of the real leaders" on the team and said he hopes to extend Hardy's one-year deal past this season.
Marshall, who was diagnosed with borderline personality disorder three years ago, had his share of emotional incidents during his time with the Chicago Bears. He told "Inside The NFL" that he even "got into it" with a Jets teammate during Sunday's 30-23 loss to New England.
"This is a sensitive topic for me because I've overcome a lot of things, and I'm really passionate about guys building character, guys really looking [at] themselves in the mirror and trying to get better," Marshall said. "Every game I know there's going to be two or three cameras in my face. Why? Because I'm a high-emotion guy and because of my history. I am aware."
On Wednesday, Marshall was asked, given his history of volatile behavior, why he's qualified to comment on Hardy.
"I'm the perfect person to talk about issues like that because I've been through it. Now I'm on the other side, so I get it. I understand it," he said.
He also said he doesn't care whether critics question him calling out Hardy.
"I don't care what people say. I know who I am," Marshall said Wednesday. "I'm proud of the person I am today."
ESPN.com Jets reporter Rich Cimini contributed to this report.