Pep Guardiola welcomed the Premier League's show of support for the Black Lives Matter movement but said "a thousand, million messages" were required.
The Manchester City manager said after a 3-0 home win over Arsenal he was "embarrassed and ashamed" by the treatment of black people.
Guardiola and his City side joined opponents Arsenal and Aston Villa and Sheffield United in taking a knee in the opening stages of their matches on Wednesday.
As the Premier League returned amid the coronavirus pandemic, players, coaches and officials copied the demonstration made famous by NFL quarterback Colin Kaepernick when he protested against social inequality and police brutality.
The issues have again come to the fore following George Floyd's death in police custody in Minneapolis last month.
Guardiola acknowledges there is still so much more to do.
"We should send a thousand, million messages for the black people," he told Sky Sports. "For centuries, 400 years, to do what we have done to these people...
"I'm embarrassed and ashamed of what the white people have done for the black people. Just because you were born with another colour of your skin, how can people think they are completely different to one another?
"All the gestures are good and positive. They are to do with facts. Things are not going to solve in a few days, but [we will do] everything we can do to make it conscious that it is not acceptable.
"In the 21st century, it is still happening, this kind of thing - not just in the USA, all around the world.
"We have to do a lot of things for the black people which we have not done so far."
Raheem Sterling, Kevin De Bruyne and Sergio Aguero were on target for City, while Arsenal's David Luiz was sent off.
The Brazilian had come on amid some early Arsenal injury problems, but the most serious issue saw City lose young defender Eric Garcia late on.
Garcia appeared to be hit in the face as he collided with team-mate Ederson.
Guardiola said: "We are really concerned. [Garcia] responded quite well but we have to wait. He is conscious, which is a good sign. We will make another test."