"If it smells like a pig, it looks like a pig and it's oinkin'," Smith said, "then guess what my friend, it's a pig."

Broncos players were irate at the end of "Thursday Night Football" ... after Jets players hit Denver QB Brett Rypien late AND hard, despite the game essentially being over at 37-28.

Things got so heated ... Broncos head coach Vic Fangio told his players to ignore postgame handshakes and go "straight to the f*cking locker room!"

And, afterward, on the NFL Network, Smith said the whole scene went down because he believes Williams is a dirty coach who instructs his players to be dirty.

"Gregg Williams is a guy who has had bounties on guys and made sure, 'Hit him when he goes out of bounds,'" Smith said ... "Wherever he goes, the nonsense follows. That's how he runs his defense and that's how he does it. Straight up."

Smith says he's seen it firsthand when he was playing in the league ... claiming players on Williams' teams would hit him late based on the instructions of the coach.

"I'm not saying you have to believe me," Smith said. "I'm saying I'm willing to put myself out there and call a spade a spade."

For the Jets' part, head coach Adam Gase told media members he basically understood why Fangio rushed his players off the field without shaking hands ... saying, "I think he was just making sure we didn’t have any kind of melee."