The celebrity and longtime environmental advocate was in Washington on Tuesday night to honor Claybrook, who recently retired as head of the watchdog group Public Citizen.
Redford honored Claybrook as a teacher, mentor and friend.
"She taught me the ropes of how to lobby and how to develop patience, which is not my virtue," Redford said in an interview, adding he met Claybrook in the early 1970s when he decided to get involved in advocacy work.
"Compromise along with patience was not kind of in my vocabulary," Claybrook later told dinner guests at the event.
One of Redford's first efforts in lobbying was trying to stop confirmation of a Cabinet nominee of President Richard Nixon. Redford said he thought he had persuaded enough lawmakers to block the nomination, but they ultimately did support the Nixon appointee.
"I was just devastated," Redford said.
He said Claybrook reacted by saying, in lobbying "you don't always lose."
"That hit me hard," he said, adding that it was Claybrook's "personal legacy" to him.
Among the Washington stars who stopped by the gathering to honor Claybrook's 27 years of leadership were House Speaker Nancy Pelosi, D-Calif., and Sen. John McCain, R-Ariz.
McCain said he hopes Claybrook will continue to be an advocate after her retirement. "I think she can be a consumer advocate in this administration, and I guarantee she would have been in mine," last year's Republican presidential nominee said to audience laughter.
The liberal consumer advocate formed an unlikely partnership with McCain when they worked together on issues such as campaign finance reform. "If it had not been for Joan Claybrook, we would have never passed that legislation," McCain said.
Claybrook told dinner guests that Public Citizen was successful because of its determination.
"One of our operating principles is that we fight back when we're attacked, and we try to have fun doing it. If you don't have some fun, it's hard. So we're scrappy, and agile and bold and creative and determined and principled and relentless."
Claybrook told stories on her tactics against opponents, including finding their own shortcomings and dirty secrets. She told how her group helped push Chrysler to put air bags in its cars. "So just keep asking, keep pushing."
Claybrook, Redford and Public Citizen founder Ralph Nader dined at the same table during the 300-person event at the Sewall-Belmont House and Museum.
Claybrook's efforts have influenced rules on auto safety standards, congressional ethics, campaign finance, drugs in the marketplace and other issues in the name of public interest.