Mack said Smith, who played two seasons for the Browns before he was released last year, committed the dirty play in the second quarter.
"I don't think he should be able to do that," Mack said Monday. "I'm still fired up about it."
Mack was so enraged by what Smith did during a running play that he started to chase him toward Kansas City's sideline before turning around because Cleveland's punt team was coming onto the field. Mack gestured to the officials and pointed at Smith, who denied any wrongdoing.
"I don't have no comment," Smith said. "I don't recall doing anything like that. I'm not known for being a dirty player or anything like that, so I don't know what that was all about."
The next time Cleveland had the ball, Mack committed an unnecessary roughness penalty when he hit linebacker Derrick Johnson after the whistle. The penalty proved costly because the Browns were backed up 15 yards and kicker Phil Dawson missed a 42-yard field goal just before halftime of Cleveland's 16-14 loss.
Mack was running downfield to block for teammate Jerome Harrison when he plowed into Johnson.
"I'm trying to rush there and get a block and do things, be fired up, play the game with passion and a little too much passion," Mack said. "It hurt my team and I feel bad for it. But I'm trying to play the game fast. It's my job to be protecting my running back, and that's what we're trying to do."