The Liverpool manager's comments come following a statement from the FA that said there is insufficient evidence to charge Firmino.
"It was a long time and I am really proud of how he dealt with it," Klopp said.
"We were sure from the first second that there is nothing to be afraid about from his side. So, happy that is confirmed now," he added.
Klopp concluded by emphasising the significance of the fight against racism: "It is a very important subject. Racism is obviously still in this world something we need to think about and we need to be careful with. But if there is nothing, then we need to sort it as well. All good now, let's carry on."