In the December 24 game, Jones made a low hit on Bengals cornerback Eli Apple, who described the incident as "a dirty play".
It came as the Bengals defense scooped up an incomplete pass and began to run it back for a touchdown. Unaware the whistle had been blown and the play was dead, both teams acted as if the ball was live.
During the return, Jones positioned himself in Apple's path and dropped at the knees to take him out of the play.
Apple accused Jones of having "done that before", after the Bengals sealed a 22-18 victory.
The NFL's official website, citing NFL Network, reported Jones was fined $13,367 for his block on Apple, plus a further $10,609 for an unnecessary roughness violation, in a separate incident, amounting to $23,976 in total.
Speaking to radio station WEEI on Monday, Jones had defended his actions by saying he was just "trying to stop a fast guy from getting to another fast guy".
"It's a split-second decision and there's a lot that goes into it," Jones said. "You're out there trying to compete, it's a physical game, so I was just trying to help the team win.
"I have all the respect for Eli and the Bengals. They played a great game. So, there's no hard feelings and definitely no intention to hurt anybody on that play.
"I get hit a lot, too. We're all out there playing hard – it's just part of the game."