Carter's was one of a number of fines announced by the league on Friday. San Diego defensive lineman Antonio Garay also was fined $15,000 for a hit below the knees of Patriots quarterback Tom Brady last Sunday.
Carter said Friday he plans to appeal the fine.
"Fed-Ex mail," Carter said when asked how he got the news. "I thought I was home free, but there ended up being a nice little letter on my seat. I kinda knew what it was. I opened it up and it notified me that I got fined."
Carter got flagged for unnecessary roughness after leading with his helmet on a hit on Rivers at 13:16 of the second quarter on Sunday.
Carter said it's the second fine of his career, noting he got fined for a late hit during the 2002 season.
"But that was a late hit," he noted. "I'll take credit for that one; that was pretty bad. It was like one thousand one, one thousand two, one thousand three and boom. Same fine, different year."
Carter said the fine won't change his approach on the field.
"No, you take your lashings and you keep ticking," he said.
Chris Forsberg covers the Patriots and Celtics for ESPNBoston.com. Information from The Associated Press was used in this report.