He said the removal of Confederate flags across the South was "a modest but meaningful balm for so many unhealed wounds" but that the US needed to go further.
"I don't think God wants us to stop there," Mr Obama said.
He urged the audience to use the killings as a spur for reforming a criminal justice system that puts one-in-three black men jailed at some point in their lives and for confronting "the unique mayhem that gun violence inflicts upon this nation".
"It would be a betrayal of everything Reverend Pinckney stood for, I believe, if we allow ourselves to slip into a comfortable silence again," he said.
Reverend Pinckney was also a South Carolina state senator and mourners from across the state and the country came to Charleston to honour his memory. One by one speakers at the funeral recalled the tall pastor with a booming voice but a kind heart and a gentle spirit.
Tim Scott, a Republican senator from South Carolina, told The Telegraph that Reverend Pinckney was "a prince of a fellow". "He was always focused on other people and as close to the embodiment of the notion of giving as I have known."
Mr Obama first met Reverend Pinckney in 2007, when the young local politician endorsed his then long-shot bid for president. Joe Biden, the vice president, had seen him within the last year in Charleston.
Both men flew to South Carolina for the funeral aboard Air Force One, accompanied by John Boehner, the Republican speaker of the House.
Mr Obama met with Reverend Pinckney's wife and two children before delivering the eulogy, which he drafted himself and was still working on in the White House on Friday morning.
He was accompanied by Michelle Obama, who also knew the Reverend Pinckney from the 2008 presidential campaign.
The funeral was far from solemn and Reverend Pinckney's fellow pastors boomed their tributes to cries of "Amen!" from the crowd. Thousands of congregants rose to their feet and swayed in unison for the gospel song "Goin' Up Yonder".
William Dudley Gregorie, a member of the Charleston council, urged the mourners to stay hopeful.
"We are a hopeful church. Because living without hope is like living in continuous darkness," he said. "But hope peers through darkness, sees the light and waits until morning."