Smith claimed that Jenkins made comments about his wife during the Panthers' 30-15 win over the Rams, a match that saw the 34-year-old score a touchdown with his 800th career catch.
Smith celebrated the score by taunting Jenkins and criticised the 24-year-old's actions after the game.
"What I don't like is a young guy who comes in, who obviously his first time ever using the Internet and Google, and he Googles information about me, talks about my wife and stuff like that. That's just some of the bullshit I just don't play with," ESPN quotes Smith as saying.
"I don't play them games. When you try to take it personal like that, I don't have any great humbling things to say. So he can take his ass back to St. Louis and watch the fucking film, 'cause I don't play them games. And if I see him on the street, I'm going to bust him in the fucking mouth. Yes, I directly pointed to him [after the touchdown]. I don't give a damn. When you embarrass people, you rub it in their face. When your dog pisses on the carpet, you rub it in his face.
"When I don't know a guy and he's talking about how's [my wife] doing, those things. A few of their guys had something to say about it, talking about I know her birth date and I did this to her. If that continues, I'm going to call some people out their names. I don't play games, I'm here to play ball. When you try to make it personal and you say stuff, I don't play that."
The Panthers moved to 3-3 with the victory and now sit second in the NFC South.