Clinton, who as president took part in MLB's ceremony retiring Jackie Robinson's No. 42 uniform number in 1997, spoke at a luncheon honoring Hall of Famer Hank Aaron, Muhammad Ali and entertainer Bill Cosby for the trio's contributions to civil rights and charitable works.
The former president told a crowd of about 1,400 at the Duke Energy Convention Center that despite such racial progress as the election of Barack Obama as president, problems remain that disproportionately hit minorities. Clinton cited unemployment, the mortgage crisis, high cost of college, and access to health care among continuing issues.
"A lot of people might be tempted to believe that the struggle — which both produced these three giants of sports and comedy and gave them the power to help so many others — that struggle for racial equality is over," Clinton said.
"But I really came here to say if you want to honor Hank Aaron and Muhammad Ali and Bill Cosby, you must first recognize that this struggle is nowhere near over," he said.
The luncheon was among events leading to Saturday night's first regular-season Civil Rights Game, between the Chicago White Sox and Cincinnati Reds.
Ali, whose long battle with Parkinson's disease has limited his physical activity, remained seated as fellow former boxing champion Sugar Ray Leonard presented him his award. Ali looked it over as his wife, Lonnie, spoke on his behalf.
Cosby had the crowd roaring during his acceptance speech, and urged the audience to make sure new generations know what Ali, Aaron and others had to overcome to be successful, and that there is more to be overcome.
"This is not a time to rest," Cosby said.
Aaron, Ali and Cosby were driven onto the field on carts before the Reds played the Chicago White Sox in the Civil Rights Game, which was held in Memphis, Tenn., the last two years. This was the first time it was held in conjunction with a major league game.
Teams wore throwback jerseys from 1964, the year that the Civil Rights Act was passed outlawing racial segregation. Hall of Famer Frank Robinson, who became a star in Cincinnati before being traded to Baltimore after the 1965 season, threw a ceremonial first pitch to Reds Hall of Famer Tony Perez.
Ali wore a Reds jersey and raised his right hand slightly, acknowledging the crowd, as he was driven along the warning track for his grand entrance to Great American Ball Park. He was helped to a chair along the first base line to watch the pregame ceremonies, which included videoboard tributes to all three.
Aaron was particularly touched by the events. He told reporters before the game that Cincinnati has always been special to him.
"My connection with Cincinnati goes back a long, long ways," said Aaron, who tied Babe Ruth's previous home run record of 714 at now-demolished Riverfront Stadium in 1974. "This is a tremendous day for me, not only to get the Beacon Award but to be back in Cincinnati."
Baseball commissioner Bud Selig said Aaron was deeply touched by the award.
"I don't think I've ever seen him as emotional as he was today," Selig said.
Major League Baseball was pleased with the weekend, which took the Civil Rights Game onto a much bigger stage for the first time.
"We're very proud of this event," Selig said. "It's come a long, long way in a short period of time."
AP Sports Writer Joe Kay in Cincinnati contributed to this report.