Parents also should have a network of people who can help look after kids who might be headed for trouble, Cosby said.
"If you're not doing that, then you should be ashamed of yourself," he said Thursday as the moderator for discussions at Xavier University on parenting, education and social responsibility.
His appearance, part of the nationwide tour "A Call Out With Cosby," also marked the 68-year-old comedian's first visit to Cincinnati since he canceled two shows following the city's race riots in 2001.
Rioting broke out after an unarmed black man was shot and killed by a white police officer trying to make an arrest. Activists then called for a boycott of the city and sent letters to entertainers, asking them to stay away until leaders agreed to pay more attention to police, racial and economic issues.
Cosby's publicist, Joel Brokaw, has said Cosby wasn't supporting the boycott, but felt it wasn't an appropriate time for comedy.
Speaking to a group of about 1,200 people at Xavier's basketball arena, Cosby emphasized points he has made in the past about parents not doing enough for their children.
Many parents know their children are misbehaving but don't do anything to stop them, he said.
"What's worse is how sedated you seem to be about making corrections," he said.
During a question-and-answer session with the audience, Cosby granted a local minister's request to speak with an 18-year-old whom the minister said had lost direction in his life.
Cosby called Rodney Lee of Cincinnati to the stage and then walked off with him. They spoke privately for nearly 45 minutes as the audience continued to question a panel of child experts.
"He asked me, 'Where do I see my life in the future?'" Lee said.