The news outlet's source requested anonymity because league had yet to announce the fine.
"We've got to get better as a National Football League," Tomlin said on Sunday. "Man, these penalties are costing people games and jobs. We've got to get them correct. So, I'm pissed."
It is believed Tomlin, who called the quality of officiating "a joke," apparently was unhappy with a questionable roughing-the-passer penalty called against Steelers linebacker T.J. Watt.
There has been an outcry around the NFL about such calls this season, as the league seems to be more intent than ever on protect its quarterbacks.
Tomlin, who is a member of the of the NFL's competition committee, on Monday spoke about the issue with Troy Vincent, the league's executive vice president of football operations, and told reporters later he did not expect to draw a fine.
"I said what I said after the game," Tomlin added. "I meant it, but I have no further comment."
Tomlin was fined $100,000 by the NFL in 2013 when he accidentally stepped onto the field during a kickoff return by Jacoby Jones of the Baltimore Ravens, who had to swerve to avoid the coach and was tackled after a 73-yard return that otherwise might have been a touchdown.
Although he was not penalized during the game for the violation,
Tomlin accepted the fine without complaint, saying he was "mesmerized" by watching the return on the video board.