Stuart claimed on Sunday he was speaking as a father not a coach when he made the comments, relating to a dispute from more than a decade ago.
Saturday night's comments in Canberra came as emotions ran high, with the Raiders' 26-6 loss to the Panthers leaving them in a tight struggle to make the NRL top eight.
"I regret saying what I did on that platform after the game," Stuart said in statement.
"I was speaking as a father and not as a football coach. My reaction was to a family situation that I thought I had dealt with, clearly I haven't.
"I allowed my emotions to get the better of me and for that I'm sorry.
"There is a history between Jaeman Salmon and my family that I will not go into.
"I should not have brought it up after the game, but it just got the better of me. I am truly sorry."
In a fiery post-match press conference, Stuart made his comments about Salmon after the 23-year-old lashed out with his leg in a tackle, his boot connecting with Raider Tom Starling's groin and face.
Salmon was given a gradeone contrary onduct charge over the incident by the match review committee on Sunday and faces a fine of $1000 with an early guilty plea.
It's believed Salmon played rugby league with Stuart's son close to 10 years ago, when Stuart was still living in the Cronulla region as coach of the Sharks.
Salmon desperately wanted to speak to media on Saturday night to give his side of the story, but was instructed not to do so by Panthers coaches.
Penrith confirmed to AAP on Sunday morning that they were in talks with the NRL and may consider legal action on their player's behalf.
The NRL was also reviewing the comments made by Stuart and considering if any punishment will follow.
