Martin also said that he expects to play for the Lions (3-6) in their home game versus the Carolina Panthers (6-3) on Sunday (1 p.m. ET).
The 28-year-old Martin was injured after being blocked by Bears wide receiver Josh Bellamy during the third quarter of Sunday's game. He remained on the ground for several moments before making his way back to the sideline.
Martin was taken via ambulance to a Chicago-area hospital, with the NFL Network reporting that he was coughing up blood at one point. The 6-foot-1, 211-pound Martin was later discharged and flew home with the team.
"It was precautionary. I'm all good. No story here," Martin said, per the Detroit Free Press. "It was just something alarming that I just went to check out. Nothing it ended up being."
When pressed for further comment, Martin did his best to put an end to the topic.
"I'm fine," Martin said. "I'll be playing Sunday. Cool?"
Martin is netting a career-low 36.6 yards per punt this season for the Lions, who rank last in the league in punt-return average (20.4 yards).