The shootings came in the wake of a particularly nasty presidential race between Clinton and presumptive Republican presidential nominee Donald Trump.
"Police officers across the country are pouring their hearts into this work because they know how vital it is for the tranquility of America", she said.
Speaking at the African Methodist Episcopal Church's conference in Philadelphia, Hillary Clinton reacted to the shooting deaths of Alton Sterling and Philando Castile and the slain Dallas police officers by summarizing this week's violence as a problem the country has to address now because "we owe our children better than this".
Clinton led conference participants in prayer, imploring them to put themselves in the shoes of police officers walking a beat or a black American stopped by a police officer.
Hillary Clinton ended her speech on Friday with a quote from the Book of Revelations.
Clinton's description of a biased and indifferent American psyche and her declaration that "something is wrong with the country" resonated with other congregants who said they were broken by the events that transpired this week and in months and years past. "Last night in Dallas, during a peaceful protest related to those killings, there was a vicious, appalling attack", she said. "For the families of those police officers who live everyday with the fear that something like this could happen and we will always be proud of their service and sacrifice", said Clinton. "And we know there is too little trust in too many places between police and the communities they are sworn to protect".
When it comes to solving the problems, Clinton asked "white Americans" to put themselves in the shoes of "black Americans", and imagine being profiled, followed around stores or anxious every time their own children left home. He instead posted a Facebook video urging people to "stand in solidarity with law enforcement, which we must remember is the force between civilization and total chaos".
"We've got to figure out what is happening when routine traffic stops, when routine arrests, escalate into killings", Clinton said. She stressed the need for police to build strong community relations and receive better training on the use of force, while also encouraging Americans to put themselves in the shoes of police officers, whose jobs require them to put themselves in harm's way. "I'm going to be talking with white people".
"We are unfortunately in the grip of some very divisive and hateful rhetoric", Clinton said.
Clinton campaigned with President Barack Obama on Tuesday and her appearance with Biden in Pennsylvania, a general election battleground state, was aimed at building party unity before the Democratic National Convention in Philadelphia.
"Racism has existed for so many years", she said. "I hope things can change".