Still announced in June that four-year-old Leah has pediatric cancer. She is currently undergoing chemotherapy.
The Bengals waived Still on Saturday and placed him on the practice squad, but the third-year pro said he understood the team's decision.
"I completely understand where they were coming from," Still said. "I can't give football 100 percent right now. In the business aspect they want guys to solely focus on football, which is understandable. We are here to win this city a Super Bowl and right now I am not in a position where I can give football 100 percent of everything I have."
While Still, who the Bengals took in the second round of the 2012 NFL draft, received offers to join other teams' practice squads, he said he wanted to remain in Cincinnati to remain closer to Philadelphia, where his daughter lives, and because he appreciates the team for standing by him during a difficult period.
"They could have just washed their hands completely of it," Still said. "Say we don't care what's going on in his personal life, we just want people who can care 100 percent on football, that's what they pay us to do. But they thought about my personal issues and allowed me to come back on the practice squad so I still have insurance."
Bengals coach Marvin Lewis said Still will "almost undoubtedly" be on the team's 53-man roster at some point.
Still, 25, has played in 17 games with Cincinnati, recording 21 combined tackled and 0.5 sacks. Former Oakland Raiders sixth-round pick Christo Bilukidi earned the final defensive tackle roster spot over Still.
- Ben Estes