"I think it's wonderful to march and to protest and it's wonderful to see all across the country, people doing it," Winfrey told PEOPLE exclusively in an interview in the magazine's new issue.
But it's not enough to march, said Winfrey, a producer and costar of the new movie Selma, about Martin Luther King's 1965 marches to support voting rights for African-Americans.
"What I'm looking for is some kind of leadership to come out of this to say, 'This is what we want. This is what has to change, and these are the steps that we need to take to make these changes, and this is what we're willing to do to get it.' "
"I think what can be gleaned from our film," said Winfrey, "is to take note of the strategic, peaceful intention required when you want real change."
David Oyelowo, who plays King, added, "And you saw that in the way black and white, young and old, came together to say, 'This is not okay.' "
But organizers and supporters of the current protests slammed Winfrey's comments. "If @oprah doesn't see 'leadership' in Ferguson, it's cuz she's not really looking. It's grass-roots – she has to do work to see the teams," wrote one Tweeter.
Many argued that activism has changed drastically since the '60s. "So does @Oprah expect someone to raise their hand at Protest when they ask 'who is your leader'? That messiah style of leadership is not us," Tweeted another person, adding, "Please direct @Oprah to read the posts under #YearOfResistance and #NewYearsRevolution if she is looking for leaders. We out here."
Concluded another: "The leaders in St. Louis are 'waiting on' you, @Oprah."
Winfrey's latest film is nominated for several Golden Globes, including best picture and best actor, and has strong Oscar buzz heading into awards season.
For more from Oprah Winfrey and David Oyelowo, pick up the latest issue of PEOPLE, on newsstands now