Television footage also showed Hardy getting into an angry shouting match with special-teams coordinator Rich Bisaccia and swiping at a clipboard Bisaccia was holding.
Hardy's animated discussion with Bryant followed immediately after Hardy broke into the special-teams huddle to berate his teammates after they gave up Dwayne Harris' 100-yard kickoff return for a touchdown that gave the Giants their winning margin, 27-20.
ESPN's Josina Anderson caught up with Bryant in the MetLife Stadium tunnel after the game and asked him about his heated exchange with Hardy.
"There is no issue," Bryant said. "That's just football. People want to make nothing into something, especially when we lose. That's just football."
Hardy issued a half-dozen "no comments" to questions in the locker room, then turned his back to the reporters.
Garrett said he thought Hardy was attempting to encourage the special-teams unit.
"I was standing right there,'' Garrett said after the Cowboys lost their fourth straight game. "To be a good football player and a good football team, you have to have passion and put it all out there. Sometimes in a game, things don't go well and you have a response. A pro football coach and a pro football team understand that those things happen. You want the guys with passion.
"It was coming off the football field. That happens, you encourage guys, you try to get guys excited. You try to get guys ready for the next challenge. I believe from my vantage point, that's what he was doing.''
Jones said he did not see the altercation, but the incident was described to him.
"As a matter of fact, I would encourage it," Jones said of Hardy's passion. "He's of course one of the real leaders on this team and he earns it. He earns it with the respect from all of his teammates. That's the kind of thing that inspires. You watched him warm up out there and he was inspirational ... nothing but warming up. He was ready to play. He's just getting guys ready to play, in my view. I don't have any issue with him being involved in motivating or pushing in any part of the football team because he plays and walks the walk."