Norman was fined $8,681 for a face mask incident and $17,363 for striking Giants wide receiver Odell Beckham Jr. in the head and neck area. ESPN contributor Jarrett Bell of USA Today Sports first reported the fines.
Norman was called for two personal foul penalties in the 38-35 Panthers win. Beckham was called for three, including a helmet-to-helmet shot at Norman, and was suspended for one game.
Norman has also appealed.
On ESPN's Mike & Mike radio show, Norman said: "The crazy part about all the unsportsmanlike conducts, I was just trying to be myself at the end of the day. I know one of those plays, I was in Cover 2, I was just jamming the man inside of the play and I got a personal foul called against me. And that was in the confines of the play, within the whistle.
"That wasn't after the whistle, that was within the whistle. ... They're probably going to send me something about that ... but I'm going to appeal it, and I'm going to get my justified case about the whole situation.
"I just pretty much showed people what this guy [Beckham] really is and what he stands for. I just don't feel like that's a part of the game that should be played. If you want to play, let's play it straight up, let's do it the right way."
According to ESPN's Stats & Info, Norman has been fined five previous times in his NFL career, but only once for something besides a uniform or a celebration violation.