Reid was flagged and thrown out in the third quarter of the 52-21 loss for attempting to tackle Steelers quarterback Ben Roethlisberger as he was sliding.
"I'm not in agreeance with what the decision was [on the ejection]," Rivera told reporters Friday. "I get the penalty. I don't get the ejection. I'm going to ask for an explanation as far as that's concerned."
NFL Officiating took to Twitter on Thursday night to explain the ruling:
That explanation apparently doesn't suffice for Rivera.
Reid, meanwhile, said he didn't understand why he was ejected:
"I didn't even know you could be ejected in the NFL. It was a bang-bang play. I was trying to do my job. I understand the NFL is trying to protect the quarterback, but when they run the ball, they're a running back.
"There's a guy running the ball, so I'm doing my job. ... If anything, there should be more [focus] on getting down earlier, so it wouldn't have to be close. I'm running full speed. I'm just trying to do my job."
Adding to his frustration, Reid said he was being drug-tested after the game for the fifth time since signing with Carolina at the end of September: "This is like the fifth time since I've been here. They're not going to catch me on anything."
Rivera said he's "got no issues" with the league's drug-testing system.
NFL spokesman Brian McCarthy issued a statement on the matter Friday morning: "Each week during the season, 10 players per club will be tested. By means of a computer program, the policy's jointly appointed Independent Administrator randomly selects before the game players to be tested. Page 5 of NFL-NFLPA policy."
Reid filed a collusion lawsuit against the NFL in May. Asked if he believes that situation has impacted the way he is officiated, he didn't rule it out.
"It's interesting," Reid noted. "I get fined. I got an interception overturned. We'll see how this appeal here goes."
Now, both Rivera and Reid will wait to see if they hear anything from the league.